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Leibniz and convergence?

  1. Apr 16, 2009 #1
    in the following question i am given the series:

    Σ((-1)^(n-1))*1/(n+100sin(n))

    and am asked if the series converges or diverges.

    as far as i know Leibniz's law for series with alternating signs states that if the series of the absolute values diverges then we check the following 2 conditions for convergence:
    #1) lim(n->infinity) An =0
    #2) An > A(n+1)

    i have managed to prove that the absolute series diverges so now i need to check the 2 conditions,

    #1) lim(n->infinity) An =0 can easily be proven so i move onto the next condition

    #2) An > A(n+1)
    since An is dependant on sin(n), how can i say for sure which is larger? since sin(n) can vary from -1 to 1, does this not mean that the series diverges??

    in my book it says that the series converges, is this a misprint on their behalf or am i missing something here???
     
  2. jcsd
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