Finding the Limit of a Complex Sequence

[Fairy111]

Homework Statement

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

Homework Equations

a(n)=[n+(-1)^n. sqrt(n)]/[(n^2 +1)^1/2]

The Attempt at a Solution

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

 

[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.

 

[Fairy111]

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

 

[Dick]

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