Use differentiation to find a power series representation for f(x) = 1/ (1+x)^2
geometric series sum = 1/(1+x)
The Attempt at a Solution
(1) I see that the function they gave is the derivative of 1/(1+x).
(2) Therefore, (-1)*(d/dx)summation(x^n) = -1/(1+x)^2
(3) Differentiating the summation gives:
However, the book is telling me that for my second step (2) I should be getting
d/dx [summation (-1)^n (x^n)].
Why is it becoming an alternating series here?