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.
Hello, elocin!
Evaluate: .$\displaystyle \lim_{n\to\infty}\sqrt{\frac{n+8}{36n+8}} $
Under the radical, divide top and bottom by $\displaystyle n.$
. . $\displaystyle \lim_{n\to\infty}\sqrt{\frac{\dfrac{n}{n} + \dfrac{8}{n}}{\dfrac{36n}{n} + \dfrac{8}{n}}} \;\;=\;\;\lim_{n\to\infty}\sqrt{\frac{1 + \dfrac{8}{n}}{36 + \dfrac{8}{n}}}$
. . $\displaystyle =\;\;\lim_{n\to\infty}\sqrt{\frac{1+0}{36 + 0}} \;\;=\;\;\sqrt{\frac{1}{36}} \;\;=\;\;\frac{1}{6}$