Question

How do you use the Nth term test on the infinite series `sum_(n=1)^ooe^2/n^3` ?

Answer 1

Well, the nth term test (divergence test) does not give us any conclusion since the posted series is convergent.

By pulling `e^2` out of the summation,
`sum_{n=1}^infty e^2/n^3=e^2sum_{n=1}^infty1/n^3`,
which is a p-series with `p=3`.
Since `p>1`, we can conclude that the series is convergent by P-Series Test.