Limits of these sequences

1. May 11, 2013

tedwillis

1. The problem statement, all variables and given/known data
Have a few limits that I'm stuck on:

a) lim n->infinity (n(n+1)^(n+1))/(n+2)^(n+2))

b) lim n->infinity (n^n/(n+3)^(n+1))

c) lim n->infinity n^(-1)^n

I've tried my best to understand what to do solve these, but can't get it. We've been given answers to standard limits, so I think we need to manipulate the above equations into a form where we can use standard limits.

2. Relevant equations
a) 1/e

b) 0

c) infinity

3. The attempt at a solution

2. May 11, 2013

haruspex

(n+1)k = nk(1+1/n)k. Apply that top and bottom. Do any of your standard limits look like (1+1/n)k (where k perhaps depends on n)?

3. May 11, 2013

christoff

There are several ways to interpret each of those sequences, largely due to them having so many exponents. You should write them up in LaTeX. Once you do that, I'll give it a go and see if I can give you a push in the right direction.

What "standard limits" do you have?