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Math Help - Series Problem

  1. #1
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    Series Problem

    I am having trouble to adding up

    1 + 100/99.9 + 100/99.8 + 100/99.7 + .....+ 100/0.1

    More generally,

    1 + 1/(1-a) + 1/(1-2a) + 1/(1-3a) + ..... + 1/(1-ka)


    My brain cells are dying very quickly, any help would be appreciated.

    (I apologize if this is in the wrong section, I'm not sure where Series should go)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by yyhow View Post
    I am having trouble to adding up

    1 + 100/99.9 + 100/99.8 + 100/99.7 + .....+ 100/0.1

    More generally,

    1 + 1/(1-a) + 1/(1-2a) + 1/(1-3a) + ..... + 1/(1-ka)


    My brain cells are dying very quickly, any help would be appreciated.

    (I apologize if this is in the wrong section, I'm not sure where Series should go)
    Start be defining u=0.1, then your series is:

    S=100/u+100/(2u)+ ... + 100/(1000u)=\frac{100}{u}(1+1/2+1/3+...+1/1000)=\frac{100}{u}H_{1000}

    where H_n is the n-th harmonic number, and H_{1000}\approx 7.485

    CB
    Last edited by CaptainBlack; March 24th 2010 at 10:50 PM.
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