- #1

RJLiberator

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## Homework Statement

I am giving the sum:

k=1 to infinity Σ(n(-1)^n)/(2^(n+1)

## Homework Equations

first term/(1-r) = sum for a geometric series

## The Attempt at a Solution

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With some manipulation of the denominator 2^(n+1) = 2*2^n I get the common ratio to be (-1/2)^n while the coefficient is k/2.

The first term is -1/4. This i am confident in.

When I apply the relevant equation, my answer is -1/6.

When I use wolfram alpha calculator the answer is -1/9.

There seems to be something wrong with my manipulation, I have a few guessed:

n/2*(-1/2)^n is my manipulation.

Is it possible to have a variable on the outside of the ratio when applying the geometric series sum? Does the geometric series sum even apply to a problem like this?

Thank you.