Question

If the series is convergent, find its sum: (n from 1 to infinity)
((n+1)/5^(n+1) -n/5^n )

Answer 1

\[\sum_{n=1}^{\infty}\left( (n+1)/(5^{n+1}) -(n/5^{n}) \right)\]

Just to clarify

Answer 2

/:)

Answer 3

Any ideas? I can't get anywhere near the answer.

Answer 4

THE SUME CONVEGES WHEN R IS r,<i1/5 since both sums aore geometruic hence the sume conveges at r<ii r<1/5. using the formulae

Answer 5

but its not a geometric series?

Answer 6

I haven't touched this material in a couple of decades - so a bit rusty :)

Here's what wolf says about it - just need to see how to get there ...

http://www.wolframalpha.com/input/?i=sum%28n%3D1%2Cinfty%2C%28n%2B1%29%2F5^%28n%2B1%29-n%2F5^n%29