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Compute the infinite sum of pi/4 up to 5 correct decimals.

I want to approximate pi/4 by using the infinite sum pi/4=((-1)^(n))/(2*n+1) from 0 to infinity. Here is my MATLAB code:

if true
  tol = 10^(-5)      %Up to five correct decimals
  d=1;               %Arbitrarily chosen, only condition is that d>tol at the start
  sn=0;              %Initial starting value
  while d>tol
    sn = ((-1)^(n))/(2*n+1);  This is the approximation for pi/4.
    d=abs(pi/4-sn);           Value that decides whether the loop continues.
    n=sn;                     I'm not sure but I want n to increase by one each     
                              time to prevent       
                              circular calculations.

Why do I get Inf+ Nani?


Why do I get Inf+ Nani?

Because of


Try each step directly at the command line and see what happens...

You need to set a value for the total of the summation of each term initially to zero and then accumulate the terms into that variable -- sn is ok for the name but you don't accumulate a sum of the terms in n, you replaced in with the individual term going forward.

To get the subsequent terms you need to increment n, that is correct --


where the n=sn; line is instead; the implementation of accumulating the summation is left for you to consider how to do that a little more...

Thank you dpb, I appreciate you're answer.

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1 Answer

Answer by Azzi Abdelmalek
on 19 Sep 2013
Edited by Azzi Abdelmalek
on 19 Sep 2013
 Accepted Answer

tol = 10^(-5)       
sn=0;              %
while d>tol
  sn = sn+(-1)^n/(2*n+1);


This is obviously a homework question. Solving it does not allow the OP to find the solution by his own.

Azzi, please do not post solutions of homework questions, because this reduces the reputation and efficiency of the forum. As a teacher on a university you should think of your colleagues, who do not want to get solutions created by others than their students.

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