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Math Help - Here are two question to be proved...

  1. #1
    Newbie findmehere.genius's Avatar
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    Here are two question to be proved...

    Well, I began with Harmonic Progression yesterday....and no sooner did I start I met with this Olympus like question(thats just for me).....maybe anyone likes to help.

    Q. If b be the harmonic mean(HM) between a and c, then prove:
    1/(b-a) + 1/(b-c) =1/c +1/a

    and one more....

    Q. If n HM's(H1, H2, H3, H4......Hn) are inserted between a and b, then prove that:
    (H1+a)/(H1-a) +(Hn+b)/(Hn-b) = 2n

    I will be thankful if I cross the olympus...with anyone's help.
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    In your case for question 1 the harmonic mean

    b = \frac{2}{\frac{1}{a}+\frac{1}{c}}
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  3. #3
    Master Of Puppets
    pickslides's Avatar
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    also the special case for 2 numbers

    b = \frac{2ac}{a+c}
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  4. #4
    Master Of Puppets
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    for 1/(b-a) + 1/(b-c) =1/c +1/a

    substitute

    b = \frac{2}{\frac{1}{a}+\frac{1}{c}} into the left hand side 1/(b-a) + 1/(b-c) and simplify...


    Hopefully your result will be

    1/c +1/a
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