1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Converging/Diverging Series

  1. Jul 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Does the series ∑[n=1,∞) sin4n / 4^n converge or diverge?

    2. Relevant equations

    Ratio Test

    lim n->∞ | a_n+1 / a_n |

    3. The attempt at a solution

    By Ratio Test.

    Let a_n = sin(4n) / 4^n


    lim n->∞ | (sin (4n+1) / 4^n+1) / (sin 4n / 4^n) |

    Skipping a few steps..

    = | (sin(4n+1)/sin(4n)) * (4^n)/(4^n * 4^1) |

    = 1/4 * lim n->∞ (sin(4n+1)/sin(4n))

    Here's my problem. How do I take the limit of (sin(4n+1)/sin(4n))? Did I do the whole problem wrong? Should I have used Root test?
    Last edited: Jul 15, 2008
  2. jcsd
  3. Jul 15, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    I don't think the limit works out, as both sines will keep on oscillating, it's just like an ordinary sine in that respect. I think you will find the root test more useful, as you suggested.
  4. Jul 15, 2008 #3
    Thank you, I will try that.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Converging/Diverging Series