Question

How do you determine whether the infinite sequence `a_n=e^(1/n)` converges or diverges?

Answer 1

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`.