Question

Does `a_n = [n(n+1)^(1/2)]/(n+n*sqrt(n))` converge?

Answer 1

`a_n` converges as `n->oo`.

Explanation:

For `n!=0`, `a_n=frac{sqrt(n+1)}{sqrt(n)+1}`.

`lim_{n->oo}a_n=1`