# Trying to solve this infinite series?

Trying to solve this infinite series??

Hey folks! I've spent hours trying to solve this and have exhausted all available resources.. I just need to be pointed in the right direction!

## Homework Statement

Compute the sum of the infinite series (I believe this is an arithmetico geometric series):
$\sum \frac{n+1}{4^{n}}$

For n=0..infinity

## Homework Equations

I know the standard way to solve a geometric series, but don't know how to solve this type of series.

## The Attempt at a Solution

I've set up something like this:
$S_{n} = \sum \frac{n+1}{4^{n}}$
I've tried multiplying by 1/4, 4 and other logical things, but am just not sure how to proceed.

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mfb
Mentor
Your expression can be written as
$$\sum_0^\infty \frac{1}{4^{n}} + \sum_1^\infty \frac{1}{4^{n}} + \sum_2^\infty \frac{1}{4^{n}} + \dots$$
(This assumes you start your sum at 0, if you start at 1 you have to modify it a bit.)

haruspex