# Math Help - Find the limit of...

1. ## Find the limit of...

Hi all,

I am trying to to find the limit of e/ (n + 1) ^(1/2) as n goes to infinity. I can't seem to find any standard limits which will help me. When i graph e/ (n + 1) ^(1/2) it goes to 0... so there must be way to show it

ArTiCk

2. Originally Posted by ArTiCK
Hi all,

I am trying to to find the limit of e/ (n + 1) ^(1/2) as n goes to infinity. I can't seem to find any standard limits which will help me. When i graph e/ (n + 1) ^(1/2) it goes to 0... so there must be way to show it

Note that as $n$ gets significantly large, $n+1\sim n$.
So $\lim_{n\to\infty}\frac{e}{\sqrt{n+1}}\sim\lim_{n\t o\infty}\frac{1}{\sqrt{n}}$.
Now as n gets significantly large, $\frac{1}{\sqrt{n}}$ tends to zero.
Thus, $\lim_{n\to\infty}\frac{e}{\sqrt{n+1}}=0$.