1. The problem statement, all variables and given/known data I am giving the sum: k=1 to infinity Σ(n(-1)^n)/(2^(n+1) 2. Relevant equations first term/(1-r) = sum for a geometric series 3. The attempt at a solution 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.