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

[Lifprasir]

Homework Statement

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

Homework Equations

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]

Check the derivative of (-x)^n again. Don't forget the chain rule.

 

[rock.freak667]

When you differentiated (-x)^n, you forgot to multiply by -1.

 

[Lifprasir]

ooooooh. thanks!