finding whether the divergence test is applicable on given sequence

Question

Find whether the divergence test is applicable for sequence $$a_{n}=e^{-\frac{6}{n}}$$If applicable, then $\displaystyle \lim_{n\rightarrow \infty}a_{n}=$

What I've tried:

I did not understand how the divergence test is applied here.

But I am getting: $$\lim_{n\rightarrow \infty}a_{n}=\lim_{n\rightarrow \infty}e^{-\frac{6}{n}}=e^{-\infty}=0$$

Can anyone please explain me how can I apply the divergence test here? Thanks.

As $n$ approaches infinity, $6/n$ approaches $0$, so $a_n$ approaches _______? — quasi, May 01 '20 at 19:54
Thanks quasi. But i did not understand is Divergence test is applicable here or not. — jacky, May 01 '20 at 19:59
Is it a series, or just a sequence? The divergence test applies to series. — quasi, May 01 '20 at 19:59
So we can say that in sequence we can not apply Divergence Test. Is i am right. — jacky, May 01 '20 at 20:01
No problem. I think at this point, you might as well delete the question. — quasi, May 01 '20 at 20:04

score 0 · Answer 1 · answered May 01 '20 at 20:33

0

Your computation is wrong. $ \lim_{n \rightarrow \infty} a_n = \lim_{n \rightarrow \infty} e^{\frac{-6}{n}} = \lim_{n \rightarrow \infty} \frac{1}{e^{\frac{6}{n}} = 0 $. And it's a sequence, you can't apply divergent test here.

answered May 01 '20 at 20:33

Itachi

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finding whether the divergence test is applicable on given sequence

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