Find the limit of the sequence

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• Jul 25th 2012, 11:47 PM
NeedsHelpPlease
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
• Jul 26th 2012, 04:24 AM
Plato
Re: Find the limit of the sequence
Quote:

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 $(-1)^n(3)^n+\frac{e^{-n}}{5n}\text{ or }\frac{(-1)^n(3)^n+{e^{-n}}}{5n}~?$
• Jul 26th 2012, 06:26 AM
HallsofIvy
Re: Find the limit of the sequence
And the "ratio test" is a test for convergence of a series, not a sequence.
• Jul 26th 2012, 06:39 AM
Prove It
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*}