So i am given (1+x)/(1-x)^2 and I have to put it into a power series. I know that 1/(1-x)= 1+x+x^2+x^3+...=∑x^n from 0 to infinity. I am having problems factoring series. I differentiate 1/(1-x). I get, 1/(1-x)^2= 1+2x+3x^2+...= ∑nX^(n-1) the sum from 1 to infinity. rewriting this equation. 1/(1-x)^2=∑(n+1)X^n. The sum from 0 to infinity. multiply both sides by (1+x) I get (x+1)/(1-x)^2 = (1+x)∑(n+1)X^(n) , from 0 to infinity. Then I distribute 1+x. ∑(n+1)X^(n) + ∑(n+1)X^(n+1) both sums have an index of 0. My problem is that I have having trouble factoring using summation notation and I am not sure how my book factored these 2 sums into 1 to get the answer ∑(2n+1)X^n with the index of 0. When I factored my previous work I got. ∑(n+1)(X^(n)[1+X] which I cannot seem to to put into the form the book has it.