Homework Help: Power Series Help

bcjochim07 · Apr 15, 2008

1. The problem statement, all variables and given/known data
Find the interval of convergence of f'(x)

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

2. Relevant 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.

bcjochim07 · Apr 15, 2008

Is the derivative the sum from n=1 to infinity of [(x-5)^(n-1) * (-1)^(n+1)]/[5^n]?????

Dick · Apr 15, 2008

bcjochim07 said: ↑

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)?

bcjochim07 · Apr 15, 2008

Oh... it should be (-1)^(n+1) in the original function, I just typed it out wrong.

Dick · Apr 15, 2008

It looks fine then.

rostbrot · Apr 15, 2008

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.

rootX · Apr 15, 2008

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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