# More limits

1. Jan 8, 2009

### Fairy111

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

What is the limit of the following sequence, if it exists?

2. Relevant equations

a(n)=[n+(-1)^n. sqrt(n)]/[(n^2 +1)^1/2]
3. The attempt at a solution

Can i use l'hopitals rule? Or if not, how should i do this particular question?

2. Jan 8, 2009

### daveyinaz

I'd imagine as $$n \rightarrow \infty$$?

In that case, looks like it's going to oscillate back and forth dwindling down to 1.

3. Jan 8, 2009

### Fairy111

Yea....as n tends to infinity. What were your steps to working out that it tends towards 1?

4. Jan 8, 2009

### Dick

Divide the numerator and the denominator by n. Think about the behavior of each term.