# Homework Help: Power Series help please

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1. Apr 24, 2017

### PhysicsCollegeGirl

1. The problem statement, all variables and given/known data

There are three problems that I am struggling with.

1. ∑[k2(x-2)k]/[3k]
2. ∑[(x-4)n]/[(n)(-9)n]
3. ∑[2k(x-3)k]/[k(k+1)]

3. The attempt at a solution

On the first two I am having problems finding the end-points of the interval of convergence. I use the ratio test.

1. ∑[k2(x-2)k]/[3k]
Here I get I = (1,3)

2. ∑[(x-4)n]/[(n)(-9)n]
I = (-13,5)

And in the last one I got the end-points but I am not sure why the left one would diverge.
It says it diverges in the answers but I cannot see it.

3. ∑[2k(x-3)k]/[k(k+1)]

I = [5/2,7/2)

I use the alternating series test to evaluate x=5/2 and it doesn't seem to go to zero. I do l'hopitals, but it always shows me that it diverges.

2. Apr 24, 2017

### FactChecker

You can tell immediately that this is wrong. The interval of convergence of this power series is centered at x=4. I could believe (3,5) but not (-13,5). (I don't know about the endpoints.)
Look at this again. The terms are (-1)k/[k(k+1)] at x=5/2.

3. Apr 25, 2017

### vela

Staff Emeritus

It would be really helpful if you showed your work. Simply writing down the wrong answer doesn't give us much to go on to figure out where your mistakes are.