# 2 in 1

1. Aug 15, 2008

### asi123

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

Hey guys, can you help me with this on please?
First one, I need to proof convergence, and the second one is to find the radius of converge.

2. Relevant equations

3. The attempt at a solution

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2. Aug 15, 2008

### Dick

For the first one, you are given the first series converges. That means a_n->infinity. Think comparison test. 1/(a_n-x)<1/(a_n-y) if x<y<a_n. How about choosing y=a_n/2?? Can you justify that? For the second one, write it as [(n+1)^n/n^n]*[1/n^z]. The first factor has a limit. What is it?

3. Aug 15, 2008

### asi123

Right, it's e. so that's mean that in order for the series to converge, x need to bigger then 1?

4. Aug 15, 2008

### Dick

Looks to me like aside from the e, it's a power series.

Last edited: Aug 15, 2008
5. Aug 16, 2008

### asi123

This are my thoughts, is this right?

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6. Aug 16, 2008

### Dick

Why do you think 1/(a_n-2) converges? Shouldn't you state a reason?

7. Aug 16, 2008

### asi123

If 1/(a_n-2) converges, than why shouldn't 1/(a_n-2) converge? I mean if a_n -> infinity than I don't think that 2 will bother him, no?

8. Aug 16, 2008

### Dick

No, the 2 won't bother him. But you still have to show that. Set up a comparison test with something you know converges. Review my hint about this one.

9. Aug 16, 2008

### asi123

Yeah, I got you, thanks.