determine whether the sequence is converging or diverging. will post question, click this please

Question

hoybaby · Answer

$$a _{n}= \frac{ e ^{n}+e ^{-n} }{ e ^{2n}-3 }$$

hoybaby · Answer

having a tough time determining

vuriffy · Answer

I believe that's converging. One second.

hoybaby · Answer

towards what exactly?

hoybaby · Answer

is it diveriging to 1? i think it is

hoybaby · Answer

because the answer format is the equation i listed but with this = (blank)

hoybaby · Answer

i tried putting that answer in the webassign but showed i was wrong

vuriffy · Answer

I'm not completely sure, it's been a few years, so I apologize that I cannot help fully.

vuriffy · Answer

It may actually be converging.

dumbcow · Answer

if you take limit as n-> infinity, the limit = 0.
Series converges to 0

$$\lim_{n \rightarrow \infty} \frac{e^n + \frac{1}{e^n}}{e^{2n} -3} = \lim_{n \rightarrow \infty} \frac{1}{e^n} (\frac{e^{2n}+1}{e^{2n}-3}) = 0*(1) = 0$$