Using a while loop to determine and display the number of terms it takes for a given series to converge within 0.01% of its exact value ((pi^2)/6)?

I'm trying to get a while loop to work to do the above and then display the error and number or iterations ran, but it doesn't seem to be working and I am getting an infinite loop. Any help? My current code is:

ER=100; 
s=0;
nn=0;
while (ER >= 0.01)
   nn_sum = (1/(nn^2));
   s = s + nn_sum; %compute the running sum       
   ER =(abs(exp((pi^2)/6)-s)/exp((pi^2)/6))*100; %Calculate error
   nn = nn + 1; %counter 
end
disp(nn-1)
disp(ER)

Answer 1

[the cyclist]

Two observations:

1. I think you want your initialization of nn to be 1, not 0. Otherwise your some is infinite immediately.
2. You have an exponentiation in your calculation of ER.

If I fix those two things, I get convergence after about 6,000 iterations.

FYI, I found those by using debug mode.

[Bryan Vaughn]

That works! Its always the littlest thing that break my code. Thanks

Answer 2

[Jose Marques]

In the first iteration, seem that nn == 0 and nn_sum == (1/nn^2) which means a zero division. Maybe you can include a if statement to fix this:

 ER=100; 
  s=0;
  nn=0;
  while (ER >= 0.01)
     if (nn ~= 0) 
          nn_sum = (1/(nn^2));
     else 
          % do something
   end
     s = s + nn_sum; %compute the running sum       
     ER =(abs(exp((pi^2)/6)-s)/exp((pi^2)/6))*100; %Calculate error
     nn = nn + 1; %counter 
  end
  disp(nn-1)
  disp(ER)