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

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Homework Help Overview

The original poster attempts to find a power series representation for the function f(x) = 1/(1+x)^2 using differentiation techniques. The problem is situated within the context of series representations in calculus.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster discusses using the power series for 1/(1-x) and its derivatives to derive the series for 1/(1+x)^2. Some participants question the differentiation process, particularly regarding the application of the chain rule and the handling of negative signs during differentiation.

Discussion Status

Participants are actively engaging with the original poster's approach, providing feedback on specific steps in the differentiation process. Guidance has been offered regarding the correct application of differentiation rules, particularly the chain rule, indicating a productive direction in the discussion.

Contextual Notes

The original poster appears to be working under the constraints of a homework assignment, which may limit the resources or methods they can utilize. There is an indication of confusion regarding the differentiation steps, which is being addressed through participant feedback.

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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