Question

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

Answer 1

Since `lim_{n to infty}|sin(n)|` does not exist,
`lim_{n to infty}|sin(n)| ne 0`

By Nth Term Test (Divergence Test), we can conclude that
`sum_{n=1}^infty sin(n)` diverges.