How to calculate this Sum :

[Jan]

This is not "one" sum, but n different sums according to the index i. Do you want a numerical or symbolical summation? Please explain,what the inputs are, what you want as output and post the code you have tried so far.

Answer 1

[Torsten]

Google "telescoping sum".

Best wishes

Torsten.

[HAli]

Hi thanks for your answer,but "telescoping sum"explain just a sum ,my problem is to solve a sum+another term!

Answer 2

[Torsten]

yes, add the other term to the value of the telescoping sum. What's the problem ?

In your case, your complete expression from above equals

l_(i)*(r_(i)+2*r_(i+1)) + r_(i)^2 - r_(n)^2

Best wishes

Torsten.

[HAli]

the problem is that I want to explain this equation in matrix form but didn't give me correct values

for i=1:n B0(i,i)=sum(-((r(i+1))^2-(r(i))^2),i,1,n)+l(i)*(r(i)+2*r(i+1)); B0(i+1,i)=-(((r(i+1))^2-(r(i))^2),i,1,n)+l(i)*(r(i)+2*r(i+1))));

        end

[HAli]

I want to find a matrix (see attachment) but with my script it doesn't work!

[HAli]

Please there is someone can help me!I would be very grateful to you

[Jan]

Please explain "it doesn't work" with any details. Letting the readers guess the details is not useful.

[HAli]

Hi Jan,thanks for your answer.First yes I want a numerical summation, because I have no unknowns in my equation, all the variables are known (l (i) = 0.042, r (1) = 0.08 and I took n = 10) and here is the last code I tried but it doesn't work!!! Thank you Jan for your help!

[Jan]

You want a numerical solution and use syms and symsum? This is a contradiction. Please explain again, what you actually want as result.

Please do not post code as screenshot, because it makes answering much easier. If I want to fix a typo in your code, I had to type it again, although you have the text available already. Rather inconvenient. Post code as text - formatted text to be exact, see https://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup#answer_18099

What is the meaning of using "for j" and then redefining "j" inside the loop by "syms j"? Of course this must fail.

[HAli]

first, yes I want a numerical solution, so what code should I use instead of "sym" and "symsum"?

second, I have this equation:(see attached) (-∑_(j=i)^(n-1)▒〖 (r_(j+1)^2-r_j^2 ) 〗+1/3 l_i (r_(i)+2r_(i+1) ))〖(w〗_(i+1)-w_(i))

and I want to exploit it in matrix form,to have a B0 matrix like this:(see attached)

Can you help me!!

Did I get a little bit to explain my problem!!

>>code

B0=zeros(n,n);

for i=1:n

            l_(i)=0.042;
            r_(i+1)=r_(i)+delta;
end

for i=1:n

    for j=i:i

        syms j n i

        f_n = symsum(-[r_(j+1)^2-r_(j)^2],j,i,n)
        B0(i,j)=f_n+(1/3)*l_(i)*(r_(i)+2*r_(i+1));  
        B0(i+1,j)=-(f_n+(1/3)*l_(i)*(r_(i)+2*r_(i+1)));        

        end

[Jan]

@HAli: I told you already how to format a message properly. I cannot reconsider, why you ignore this hint about making your question more readable.

An example for calculating a sum:

S = 0;
for j = i:n - 1
  S = S + r(j+1)^2 - r(j)^2;
end

I do not have any idea where you get terms like

B0(i,j)=f_n+(1/3)*l_(i)*(r_(i)+2*r_(i+1));

from. Such terms do not appear in the shown equation.

[HAli]

I'm sorry Jan, but I try my best !!

you told me where the term came from: B0(i,j)=f_n+(1/3)*l_(i)(r_(i)+2*r_(i+1));*

Because these are the terms of my Matrix that I named B0 : its not just a sum,but a sum (from i to n-1) + another terme just depends on i

So,for the first term of the matrix B0, I have these terms analytically:

So,I changed the code another time, using your proposal:

 B0=zeros(n,n);
for i=1:n
            l(i)=0.042;
            r(i+1)=r(i)+delta;
end

 S=0;
for i=1:n
for j=i:i
    for k=i:n-1
        S = S+r(k)^2-r(k+1)^2;
        B0(i,j)=S+(1/3)*l(i)*(r(i)+2*r(i+1));  
        B0(i+1,j)=-(S+(1/3)*l(i)*(r(i)+2*r(i+1)));        

    end
       end
end

but this program is not correct because it doesn't sum up in a correct way,he had to make the sum of r(k)^2 -r(k+1)^2 from i (the value of i depends on the line i of the matrix) to n-1 (+) the second term which (1/3)*l(i)*(r(i)+2*r(i+1) depends just on the line i of the matrix.

For example,for line i =3 of the matrix B0:

it has to sum the r(k)^2 -r(k+1)^2 of i = 3 to n-1 and add the second term (1/3)*l(i)*(r(i)+2*r(i+1) just for i = 3

N.B:I changed the variable of the sum j by k because the matrix is always defined by i (the rows) and j (columns),

[HAli]

is it always, I could not explain my problem!

Answer 3

[HAli]

please I need help to implement this formula on Matlab!!! this is the script that I did but it doesn't work!!!! Any help!!