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

1. Feb 16, 2013

### Lifprasir

1. The problem statement, all variables and given/known data
Use differentiation to find a power series representation for
f(x)=1/(1+x)2

2. Relevant equations

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 16, 2013

### Dick

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

3. Feb 16, 2013

### rock.freak667

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

4. Feb 16, 2013

### Lifprasir

ooooooh. thanks!