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Power Series Help

  • Thread starter bcjochim07
  • Start date
  • #1
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1. Homework Statement
Find the interval of convergence of f'(x)

f(x) Sum from n=1 to infinity [(x-5)^n*(-1)^n]/[n5^n]



2. Homework Equations



3. The Attempt at a Solution

My problem is I am unsure how to take the derivative with the n's and x's should I treat n as a constant?

After that, I think I can get the interval of convergence.
 

Answers and Replies

  • #2
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Is the derivative the sum from n=1 to infinity of [(x-5)^(n-1) * (-1)^(n+1)]/[5^n]?????
 
Last edited:
  • #3
Dick
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Is the derivative the sum from n=1 to infinity of [(x-5)^(n-1) * (-1)^(n+1)]/[5^n]?????
Almost. How did (-1)^n become (-1)^(n+1)?
 
  • #4
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Oh... it should be (-1)^(n+1) in the original function, I just typed it out wrong.
 
  • #5
Dick
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It looks fine then.
 
  • #6
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yes you just treat n as a constant.

Be careful when taking the derivative of a series though. Here the issue didn't come up, but if you have x^n where n starts at 0 and end up with x^(n-1) where n starts at 0 then you would get x^(-1) for n=0 which is a no-no so you'd have to move you n up to starting at 1 do solve that problem.
 
  • #7
351
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I think finding R for the original function should be enough; differentiation does not change R.

Using this way, you get R = 5?
 

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