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

  • Thread starter Lifprasir
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  • #1
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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) = [itex]\sum[/itex](x)n
1/(1-(-x)) = [itex]\sum[/itex](-x)n

Deriving 1/(1-(-x))
-1/(1-(-x))2= [itex]\sum[/itex]n(-x)n-1 from n=1 to infinity

indexing it from n=0,
[itex]\sum[/itex](n+1)(-x)n

finally,

(-1)*-1/(1-(-x))2 = -[itex]\sum[/itex](n+1)(-x)n

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

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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619
Check the derivative of (-x)^n again. Don't forget the chain rule.
 
  • #3
rock.freak667
Homework Helper
6,223
31
When you differentiated (-x)^n, you forgot to multiply by -1.
 
  • #4
16
0
ooooooh. thanks!
 

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