- #1

icesalmon

- 270

- 13

## Homework Statement

Determine the Convergence or Divergence of [tex]\sum_{n=1}^\infty\left(sin(1/n)\right)[/tex]

## Homework Equations

limit comparison test

## The Attempt at a Solution

I don't know what to compare this series to, I tried the harmonic series to get sin(1/n)/(1/n) = nsin(1/n) which is just an infinity that oscilates. Which I believe to be divergent.

I've been really confused about a lot of comparisons because I'm only aware of a handful of series that converge or diverge the harmonic series (1/n) another series (1/n^2) which converges to pi

^{2}/6 p: series which if p > 1 it converges if 0 < p < 1 the p series diverges, geometric series which converge according to the formula a

_{1}/ (1 - r) if 0 < |r| < 1 and diverges if |r| > 1 And the Telescoping Series which converge according to the terms that cancel out in the set of real numbers it generates.