Question

Converge or Diverge? Summation n=1 to Inf of Sin(1/n)

Answer 1

I put it into Wolfram Alpha and it said it diverges by the comparison test. I'm not sure what to compare it to since I'm sleepy and need a nap. Good luck!

Answer 2

Diverge. Consider the Maclaurin expansion for sin x (in the attached for convenience). For small values of angle this function is essentially equal to the angle. Then the comparison can be made with the series whose terms are 1/n.