Hello MatLab /C++ gurus out there,

Its in no way complete and hasn't been verified but should be enough of a pointer to get you in the right track if using Matlab:

clear
clc
N = 2;
e = 100;
e1 = 10^-5;
piii(1)= 1/0.75;
while e >= e1
pii=0;
for k=1:N
piii1= ((-1)^(k+1))/(0.5*k-0.25);
pii=piii1+pii;
end
piii(N)=pii;
e=abs(piii(N)-piii(N-1))/piii(N-1);
N=N+1;
end

On a second note you could tell the Prof., " I can use pi function of Matlab to get the damn number, why worry about doing the homework"

Here is the code. It is perfectly running and does converge to 3.1416 for e=10^-8 with N= 63661979. Do the same for 10^-1 thru 10^-8. Hope you know how to make plots after this. Make sure the name of mat-file is pii.m and enjoy!!!!

Thank you very much F22 and Santosh1984. I was dying to get the right answer...