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I have problem figuring out if this series is convergent or divergent. Please help!

$\sum_{n=1}^{\infty} \frac{1}{\exp(1/n)}$

Thanks

2 Answers 2

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as n goes to infinity , $ e^{\frac{1}{n}} $ goes to 1. So your limit of summand goes to 1.. Therefore it should be divergent.

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    It's just the same result, @ZachL.2012-11-07
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I'd use the Divergence Test to show that this infinite series diverges.

The theorem states that if a series ${a_n}$ does not converge to $0$, then $\sum_{n=1}^{\infty} a_{n}$ diverges.

$\lim_{n\to\infty}\frac{1}{e^{\frac{1}{n}}} = \frac{1}{e^0} \to 1 \ne0 \implies a_{n} \ \ \text {diverges}$