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Positive term series

  1. Aug 10, 2009 #1
    sum(1/(n(n^2-1)^(1/2)),n=2,infinity)
    first derivative <0 for x>=2
    I(1/(x(x^2-1)^(1/2)),x,2,infinity)
    x=secT, dx=secTtanT
    I(secTtanT/(secTtanT),T) ?
     
    Last edited: Aug 10, 2009
  2. jcsd
  3. Aug 10, 2009 #2

    Cyosis

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    What is your question?
     
  4. Aug 10, 2009 #3
    my book is showing this series converging to pi/6
     
  5. Aug 10, 2009 #4
    ok..this integral is in basic form of I(1/(u(u^2-a^2)^(1/2)),u)=1/a sec^-1(u/a)+C
    a=1
    sec^-1 u
    lim sec^-1x as x-> infinity =pi/2 and sec^-1 2=pi/3
    pi/2-pi/3 =pi/6
     
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