How do you determine whether the infinite sequence $a_{n} = e^{\frac{1}{n}}$ $a_n=e^(1/n)$ converges or diverges?

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Answer 1 · 2014-10-01T23:55:10

Let us evaluate the limit.

$lim_{n to infty}a_n=lim_{n to infty}e^{1/n}$

by squeeze the limit into the exponent,

$=e^{lim_{n to infty}1/n}=e^{1/infty}=e^0=1$

Hence, the sequence converges to $1$ .

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