Question

Limit of a series
I have a series which I can find both an upper and lower limit and I can spot is monotonic (in this case, always decreasing) but how do I go about finding the limit?

Answer 1

\[\lim_{x \rightarrow \infty} 2^{n}/(3^{n}+1)\]

Answer 2

upper limit would be the 1st term in the sequence, and a lower limit would be zero as it is never negative

Answer 3

Ok, first thing I notice, this is not a series, just a limit. Maybe you made a typo? Also the limit says x to infinity, should be n?

Answer 4

right, it's actually a sequence

Answer 5

So it's bounded between 0 and 1.

Answer 6

Let's use this: \[\frac{2^n}{3^n+1}<\frac{2^n}{3^n}\]