# Thread: Find the limit of the sequence

1. ## Find the limit of the sequence

The problem says to find the limit of the sequence.

an = (-1)n * (3n + e-n/5n)

I'm not sure how to approach this problem. Do I use the ratio test?
I apologize for the formatting. I'm not sure how to make the fraction look nice

2. ## Re: Find the limit of the sequence

Originally Posted by NeedsHelpPlease
The problem says to find the limit of the sequence.
an = (-1)n * 3n + e-n/5n
We cannot help if we cannot read the question.

Is it $(-1)^n(3)^n+\frac{e^{-n}}{5n}\text{ or }\frac{(-1)^n(3)^n+{e^{-n}}}{5n}~?$

3. ## Re: Find the limit of the sequence

And the "ratio test" is a test for convergence of a series, not a sequence.

4. ## Re: Find the limit of the sequence

Actually there is a ratio test for sequences as well.

For a sequence \displaystyle \begin{align*} \left\{ a_n \right\} \end{align*}, the ratio test states

\displaystyle \begin{align*} \lim_{n \to \infty}\left| \frac{a_{n+1}}{a_n} \right| = L < 1 \implies \lim_{n \to \infty}a_n = 0 \end{align*}