Hello , by matlab , compute the product of :
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p1=sqrt(2)/2 , p2=sqrt(2+sqrt(2))/2 , p3=sqrt(2+sqrt(2+sqrt(2)))/2 ,
compute product by matlab, p1 * p2* p3 *........... * p20
5 Comments
Jan
on 3 May 2011
Do you have a question concerning Matlab? What have you tried so far and where did the problems occur?
Walter Roberson
on 3 May 2011
Say... what does the keyword "fsolve" have to do with the question?
Matt Tearle
on 4 May 2011
The OP wants us to "solve" the problem. Duh. (I leave the "f" part as an exercise for the reader.)
Sean de Wolski
on 4 May 2011
F* solving it, Matt?
Walter Roberson
on 4 May 2011
"Fer Sure"??
Answers (3)
Walter Roberson
on 2 May 2011
function t66 = prod_p1_p20
V = 2;
t1 = V ^ V;
t3 = t1 ^ V;
t4 = t3 ^ V;
t5 = t4 ^ V;
t6 = V^(-1);
t7 = V^t6;
t11 = (V + t7)^t6;
t14 = (V + t11)^t6;
t16 = (V + t14)^t6;
t19 = (V + t16)^t6;
t23 = (V + t19)^t6;
t25 = (V + t23)^t6;
t28 = (V + t25)^t6;
t30 = (V + t28)^t6;
t33 = (V + t30)^t6;
t38 = (V + t33)^t6;
t40 = (V + t38)^t6;
t43 = (V + t40)^t6;
t45 = (V + t43)^t6;
t48 = (V + t45)^t6;
t52 = (V + t48)^t6;
t54 = (V + t52)^t6;
t57 = (V + t54)^t6;
t59 = (V + t57)^t6;
t62 = (V + t59)^t6;
t66 = t62 * t59 * t57 * t54 * t52 * t48 * t45 * t43 * t40 * t38 * t33 * t30 * t28 * t25 * t23 * t19 * t16 * t14 * t11 / t7 / t5 / t1 / V;
end
9 Comments
Abdulfattah lulu
on 2 May 2011
Oleg Komarov
on 2 May 2011
What's not clear to you?
Abdulfattah lulu
on 2 May 2011
Abdulfattah lulu
on 2 May 2011
Abdulfattah lulu
on 2 May 2011
Abdulfattah lulu
on 2 May 2011
Walter Roberson
on 2 May 2011
The function is prod_p1_p20 and t66 is the output. If you run the function, then the output will be exactly the quantity you were asked to calculate, and thus this function *is* a solution to the problem as stated. There was nothing in the problem statement that required that the variable names p1, p2, and so on, were used in the solution: the problem statement only required that the product of the quantities be found.
Go through the logic step by step. The only "tricky" part of this logic is in computing the denominator.
John D'Errico
on 3 May 2011
Crystal clear.
Walter Roberson
on 4 May 2011
Abdulfattah: how would you calculate any one p(n)? If you know p(n-1) how would you extend it to p(n) ?
Matt Tearle
on 4 May 2011
disp(1*0.6366)
5 Comments
Sean de Wolski
on 4 May 2011
Surely you meant:
disp(1*pi/4.734) %?
Walter Roberson
on 4 May 2011
Read the problem statement, Matt. *Compute* the product, not *display* the product. And the value displayed is nearly 2E-5 wrong compared to what would be computed.
Walter Roberson
on 4 May 2011
Sean, re-check that output!
John D'Errico
on 4 May 2011
Well, arguably, multiplying by 1 makes it a computation.
Matt Tearle
on 4 May 2011
Exactly, John. And there was no specification of accuracy. So I claim that my answer computes the product requested (just to 4 dp, that's all).
John D'Errico
on 4 May 2011
0 votes
Well, for complete overkill...
disp(0 + 0.63661977236781944823166583843277598162106456255690961760282370334657710024147820303991996854856502247043508070567897809925678676832984935864030869184975575167078632289509242155624801993112605554672293135860993145476492852903886184623882769012238145575770975998129003396352798880718475639573387445219320317598093723758568037151319811216067649754946716309234535128512187466093946760854635939038744626459238525652130733923947876362385118364006093735040924909121572691582778720782038355177247697778990109)
Walter - this IS a computation, as I added 0 to the result.
6 Comments
Sean de Wolski
on 4 May 2011
John, I'm disappointed in that offering. This is begging for your vpi class:
X = 1*vpi('636619772367819448231665838432775981621064562556909617602823703346577100241478203039919968548');
vpi2English(X)
ans =
six hundred thirty six novemvigintillion, six hundred nineteen octovigintillion, seven hundred seventy two septenvigintillion, three hundred sixty seven sexvigintillion, eight hundred nineteen quinvigintillion, four hundred forty eight quattuorvigintillion, two hundred thirty one trevigintillion, six hundred sixty five duovigintillion, eight hundred thirty eight unvigintillion, four hundred thirty two vigintillion, seven hundred seventy five novemdecillion, nine hundred eighty one octodecillion, six hundred twenty one septendecillion, sixty four sexdecillion, five hundred sixty two quindecillion, five hundred fifty six quattuordecillion, nine hundred nine tredecillion, six hundred seventeen duodecillion, six hundred two undecillion, eight hundred twenty three decillion, seven hundred three nonillion, three hundred forty six octillion, five hundred seventy seven septillion, one hundred sextillion, two hundred forty one quintillion, four hundred seventy eight quadrillion, two hundred three trillion, thirty nine billion, nine hundred nineteen million, nine hundred sixty eight thousand, five hundred forty eight
Walter Roberson
on 4 May 2011
Interesting how close the answer is to 2/Pi; I wonder if 2/Pi would be the limit of the product?
Matt Fig
on 4 May 2011
For example:
http://en.wikipedia.org/wiki/Vi%C3%A8te%27s_formula
John D'Errico
on 4 May 2011
Sean - Well, I did generate the result using my new floating point arithmetic class. But this brings up a good question. Can I (should I?) write a float to english converter?
John D'Errico
on 4 May 2011
Walter - I tried to verify that. Using a good approximation of pi that is sufficiently accurate for many school boards...
pi = 3;
2/pi
ans =
0.6666666666666667
Can you help me here? It seems to give the wrong answer.
Sean de Wolski
on 4 May 2011
Absolutely! Couldn't you just add 'ths to the end of each of the suffix and reverse the order? I.e. tenths hundredths thousandths etc...
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on 2 May 2011
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