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## Homework Statement

Use differentiation to find a power series representation for f(x) = 1/ (1+x)^2

## Homework Equations

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:

(-1)*[summation (n)x^(n-1)]

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?