Find the sum of the following series:
1 + 4/7 + 9/49 + 16/343 + .......... to infinity
I have a more general solution of this kind of problems.
Assume that fn(x)=Sum(k^n*x^k), for k=1,..,Inf
We alreday know that f0(x)=Sum(x^k)=s/(1-s)
So, f1(x)=s/(1-s)^2, and f2(x)=s*(1+s)/(1-s)^3
We have 1+4/7+9/49+...=7*Sum(k^2*(1/7)^k)=7*f2(1/7)=
I hope you enjoyed it!!!
Posted by George
on 2006-03-21 19:30:42