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Convergence of sin(1/n)

  1. Dec 16, 2006 #1
    Okay, this is my last problem today. I swear.

    1. The problem statement, all variables and given/known data

    For this problem, I need to find the convergence of the sum of sin(1/n) from n=1 to infinity.

    2. Relevant equations


    3. The attempt at a solution

    I know that this has to converge, but I'm having a hard time proving it. It seems like I should either be using the limit comparison test or just the comparison test, but I can't think of whta I can compare it to.
  2. jcsd
  3. Dec 16, 2006 #2
    This is very counter-intuitive. I just tried the limit comparison test with 1/n as follows:

    lim sin(1/n) = cos(1/n) * -1/n^2 = cos(1/n) = 1
    n->inf 1/n = -1/n^2

    That means that sin(1/n) must diverge. Is this right?
  4. Dec 16, 2006 #3


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    Homework Helper

    I don't follow anything from your second post, except the conclusion, which is correct. But please describe more clearly how you arrived at it.
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