- #1
RJLiberator
Gold Member
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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.