1. ## Sequences: Finding limits

HI! The problem is: an= The square root of (n+8) over (36n+8). Find the limit as n goes to infinity of an. Thank you!!! I think it converges but I can't find the limit.

2. Originally Posted by elocin
HI! The problem is: an= The square root of (n+8) over (36n+8). Find the limit as n goes to infinity of an. Thank you!!! I think it converges but I can't find the limit.
Is this supposed to be
$\lim_{n \to \infty} \frac{\sqrt{n + 8}}{36n + 8}$
or
$\lim_{n \to \infty} \sqrt{\frac{n + 8}{36n + 8}}$

They both exist but are different numbers.

-Dan

3. Hello, elocin!

Evaluate: . $\lim_{n\to\infty}\sqrt{\frac{n+8}{36n+8}}$

Under the radical, divide top and bottom by $n.$

. . $\lim_{n\to\infty}\sqrt{\frac{\dfrac{n}{n} + \dfrac{8}{n}}{\dfrac{36n}{n} + \dfrac{8}{n}}} \;\;=\;\;\lim_{n\to\infty}\sqrt{\frac{1 + \dfrac{8}{n}}{36 + \dfrac{8}{n}}}$

. . $=\;\;\lim_{n\to\infty}\sqrt{\frac{1+0}{36 + 0}} \;\;=\;\;\sqrt{\frac{1}{36}} \;\;=\;\;\frac{1}{6}$

4. It is the second one! It's the square root over the entire fraction! Thanks!