Compute the limit of the sequence
(3^n)/ ((2^n)+1)
I have simplified a much harder problem to this limit and i am having a mind blank... helpplease? cheers
Hello, sebjory!
Yet another approach . . .
$\displaystyle \lim_{n\to\infty} \frac{3^n}{2^n + 1} $
Divide top and bottom by $\displaystyle 3^n\!:\;\;\frac{\frac{1}{3^n}\cdot3^n}{\frac{1}{3^ n}(2^n+1)} \;=\;\frac{1}{\frac{2^n}{3^n} + \frac{1}{3^n}} $
Therefore: .$\displaystyle \lim_{n\to\infty}\left[\frac{1}{\left(\frac{2}{3}\right)^n + \frac{1}{3^n}}\right] \;=\; \frac{1}{0+0} \;=\;\infty$