Math Help - Limit

1. Limit

Evaluate:
$
\lim_{n\to \infty}(\frac{1}{\sqrt {n^2}} +\frac{1}{\sqrt {n^2+1}} +\frac{1}{\sqrt{n^2+2}} +.........+\frac{1}{\sqrt{n^2+2n}})$

2. Originally Posted by pankaj
Evaluate:
$
\lim_{n\to \infty}(\frac{1}{\sqrt {n^2}} +\frac{1}{\sqrt {n^2+1}} +\frac{1}{\sqrt{n^2+2}} +.........+\frac{1}{\sqrt{n^2+2n}})$
As each of the denominators get larger and larger, we see that each of those terms approach zero.

So, $
\lim_{n\to \infty}(\frac{1}{\sqrt {n^2}} +\frac{1}{\sqrt {n^2+1}} +\frac{1}{\sqrt{n^2+2}} +.........+\frac{1}{\sqrt{n^2+2n}})$
$= 0+0+0+\dots+0=\color{red}\boxed{0}$

Does this make sense?

--Chris

3. Answer is given as 2.