Series representation of 1/(x+1)^2

Homework Statement

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

The Attempt at a Solution

1/(1-x) = $\sum$(x)n
1/(1-(-x)) = $\sum$(-x)n

Deriving 1/(1-(-x))
-1/(1-(-x))2= $\sum$n(-x)n-1 from n=1 to infinity

indexing it from n=0,
$\sum$(n+1)(-x)n

finally,

(-1)*-1/(1-(-x))2 = -$\sum$(n+1)(-x)n

However, in the book, the answer is $\sum$(n+1)(-x)n. What am I forgetting? Thank you.

Dick