The problem says to find the limit of the sequence.

a_{n}= (-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

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- Jul 25th 2012, 10:47 PMNeedsHelpPleaseFind the limit of the sequence
The problem says to find the limit of the sequence.

a_{n}= (-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, 03:24 AMPlatoRe: Find the limit of the sequence
- Jul 26th 2012, 05:26 AMHallsofIvyRe: Find the limit of the sequence
And the "ratio test" is a test for convergence of a

**series**, not a sequence. - Jul 26th 2012, 05:39 AMProve ItRe: Find the limit of the sequence
Actually there is a ratio test for sequences as well.

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

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