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

Lifprasir
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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= \sumn(-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.
 
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Check the derivative of (-x)^n again. Don't forget the chain rule.
 
When you differentiated (-x)^n, you forgot to multiply by -1.
 
ooooooh. thanks!
 
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