Power Series Expansion

  • Thread starter tak13
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  • #1
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Homework Statement



I am doing this multiplication with power series and I am just stuck at this one and other questions that similar to this one.
http://img5.imageshack.us/img5/9526/img1261r.jpg [Broken]

Homework Equations





The Attempt at a Solution



It seems that I suppose to add n-k wherever I see a "n" but it doesn't seem right.
The highlighted part is the part where I stuck.
The answer for this problem is the one that I circled.
 
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Answers and Replies

  • #2
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There should be a double sum there, with a sum over k from k = 0 to n. Then you should be able to just solve what that sum would be.
 
  • #3
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Ah yes, I know the part I highlighted should have the Sum of N parenthesis then the Sum of K but I don't know how they get to that answer.
 
  • #4
SammyS
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The Attempt at a Solution



It seems that I'm supposed to add n-k wherever I see a "n" but it doesn't seem right.
The highlighted part is the part where I stuck.
The answer for this problem is the one that I circled.
What do you get if you multiply the first few terms of f(x) times the first g(x) ?

(fg)(x) = (1 + 2(x-2) + 3(x-2)2 + 4(x-2)3 + ... ) (1 + (x-2) + (x-2)2 + (x-2)3 + ...)

What is the "k" in your sum?
 
  • #5
LCKurtz
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You are using the Cauchy product:

[tex](\sum_{n=0}^\infty a_nx^n)(\sum_{n=0}^\infty b_nx^n)=(\sum_{n=0}^\infty c_nx^n)[/tex]

where

[tex]c_n = \sum_{k=0}^n a_kb_{n-k}[/tex]

In your case ak = k+1 and bk = 1. Figure out what you get for cn.
 

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