# Finding the limit of a sequence

1. Aug 17, 2014

### Caiti

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

How do you determine if the limit of (1+1/n^2)^(n^2) exists and what it is?
This cannot use logarithms at any point.

2. Relevant equations
(1+1/n)^n --> e

3. The attempt at a solution

Let N=n^2
Given (1+1/N)^N --> e, then (1+1/n^2)^(n^2) must --> e also.
Is this allowed though? Do I need to put restrictions on N?
I was thinking that I might need to show that N and n^2 have the same limit on their own, but since I have created N, it's limit is obviously that of n^2.

2. Aug 17, 2014

### Simon Bridge

Which limit do you mean?
... I cannot tell what the person marking you work will or will not allow. It is OK mathematically - except you need the "lim" part of the notation.

3. Aug 17, 2014

### HallsofIvy

Staff Emeritus
Yes, the limit of N is the same as the limit of $n^2$ as n goes to infinity. And what is that limit? It's pretty obvious but you should say it.

4. Aug 17, 2014

### Caiti

I think it would go to e.