{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":52125,"title":"Compute the sum of reciprocals of quadratics","description":"Write a function to compute the following sum:\r\n\r\nSee also Cody Problem 46000.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.008px 7.79167px; transform-origin: 143.008px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following sum:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y = sum(1/(n^2+an+b),{n,1,infinity})\" style=\"width: 122.5px; height: 45px;\" width=\"122.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.175px 7.79167px; transform-origin: 29.175px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee also \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 46000\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sumRecipQuad(a,b)\r\n  y = sum(1/(n^2+a*n+b));\r\nend","test_suite":"%%\r\na = 3;\r\nb = 2;\r\ny_correct = 1/2;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 5;\r\nb = 6;\r\ny_correct = 1/3;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 7;\r\nb = 10;\r\ny_correct = 47/180;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 8;\r\nb = 15;\r\ny_correct = 9/40;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 10;\r\nb = 21;\r\ny_correct = 319/1680;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 9;\r\nb = 14;\r\ny_correct = 153/700;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 13;\r\nb = 22;\r\ny_correct = 42131/249480;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 14;\r\nb = 33;\r\ny_correct = 32891/221760;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 12;\r\nb = 35;\r\ny_correct = 13/84;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 16;\r\nb = 55;\r\ny_correct = 20417/166320;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 15;\r\nb = 26;\r\ny_correct = 605453/3963960;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 16;\r\nb = 39;\r\ny_correct = 485333/3603600;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 18;\r\nb = 65;\r\ny_correct = 323171/2882880;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 20;\r\nb = 91;\r\ny_correct = 30233/308880;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 24;\r\nb = 143;\r\ny_correct = 25/312;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 21;\r\nb = 38;\r\ny_correct = 158899519/1319157840;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 24;\r\nb = 95;\r\ny_correct = 19622959/217273056;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 30;\r\nb = 209;\r\ny_correct = 11171129/169303680;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 36;\r\nb = 323;\r\ny_correct = 37/684;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 25;\r\nb = 46;\r\ny_correct = 265842403/2498640144;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\nc = randi(50);\r\na = 2*c+1;\r\nb = c*(c+1);\r\ny_correct = 1/(c+1);\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\nfiletext = fileread('sumRecipQuad.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assignin'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2021-07-03T14:09:11.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-06-27T14:48:37.000Z","updated_at":"2026-01-09T19:12:11.000Z","published_at":"2021-06-27T14:53:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following sum:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = sum(1/(n^2+an+b),{n,1,infinity})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\sum_{n=1}^\\\\infty \\\\frac{1}{n^2+an+b}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee also \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 46000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":52125,"title":"Compute the sum of reciprocals of quadratics","description":"Write a function to compute the following sum:\r\n\r\nSee also Cody Problem 46000.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.008px 7.79167px; transform-origin: 143.008px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following sum:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y = sum(1/(n^2+an+b),{n,1,infinity})\" style=\"width: 122.5px; height: 45px;\" width=\"122.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.175px 7.79167px; transform-origin: 29.175px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee also \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 46000\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sumRecipQuad(a,b)\r\n  y = sum(1/(n^2+a*n+b));\r\nend","test_suite":"%%\r\na = 3;\r\nb = 2;\r\ny_correct = 1/2;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 5;\r\nb = 6;\r\ny_correct = 1/3;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 7;\r\nb = 10;\r\ny_correct = 47/180;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 8;\r\nb = 15;\r\ny_correct = 9/40;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 10;\r\nb = 21;\r\ny_correct = 319/1680;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 9;\r\nb = 14;\r\ny_correct = 153/700;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 13;\r\nb = 22;\r\ny_correct = 42131/249480;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 14;\r\nb = 33;\r\ny_correct = 32891/221760;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 12;\r\nb = 35;\r\ny_correct = 13/84;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 16;\r\nb = 55;\r\ny_correct = 20417/166320;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 15;\r\nb = 26;\r\ny_correct = 605453/3963960;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 16;\r\nb = 39;\r\ny_correct = 485333/3603600;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 18;\r\nb = 65;\r\ny_correct = 323171/2882880;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 20;\r\nb = 91;\r\ny_correct = 30233/308880;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 24;\r\nb = 143;\r\ny_correct = 25/312;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 21;\r\nb = 38;\r\ny_correct = 158899519/1319157840;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 24;\r\nb = 95;\r\ny_correct = 19622959/217273056;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 30;\r\nb = 209;\r\ny_correct = 11171129/169303680;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 36;\r\nb = 323;\r\ny_correct = 37/684;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\na = 25;\r\nb = 46;\r\ny_correct = 265842403/2498640144;\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\nc = randi(50);\r\na = 2*c+1;\r\nb = c*(c+1);\r\ny_correct = 1/(c+1);\r\nassert(abs(sumRecipQuad(a,b)-y_correct)\u003c1e-15)\r\n\r\n%%\r\nfiletext = fileread('sumRecipQuad.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assignin'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2021-07-03T14:09:11.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-06-27T14:48:37.000Z","updated_at":"2026-01-09T19:12:11.000Z","published_at":"2021-06-27T14:53:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following sum:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = sum(1/(n^2+an+b),{n,1,infinity})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\sum_{n=1}^\\\\infty \\\\frac{1}{n^2+an+b}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee also \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 46000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"analytical\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"analytical\"","current_player":null,"sort":"map(difficulty_value,0,0,999) 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