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Can someone please explain leibniz rule to me,

  1. Apr 16, 2009 #1
    according to leibniz, if i have a series (An) with an alternating sign, in order for the series to converge, i need either |An| to converge, or |An| to diverge and An=0(for n->infinity) and A(n)>A(n+1)

    BUT in the following series where An= ((-1)^(n-1))*1/(n+100sin(n)) the series |An| diverges, lim An=0 BUT how can i prove that An>An+1, in fact i dont think that it is true since sin(n) goes from -1 to 1, so an could be An<An+1, YET this series converges(according to the answer in my book). can anyone see how this is possible??

    i thought that maybe the rule for An>An+1 is also for (n->infinity) but then i get An=An+1 so the rule still doesnt hold.

    can anyone please give me the exact rule here, as well as explaining why this is not working.for me
     
  2. jcsd
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