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Math Help - Ratio and Proportion II

  1. #1
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    Ratio and Proportion II

    If a,b,c,d are continued proportion : Prove that : (\frac{a-b}{c}+\frac{a-c}{b})^2-(\frac{d-b}{c}+\frac{d-c}{b})^2=(a-d)^(\frac{1}{c^2}-\frac{1}{b^2})^2


    After solving LH.S I got : \frac{2(a-d)}{(bc)^2}


    But after solving R.H.S I am getting \frac{(a-d)^2(b^2-c^2)}{(bc)^2}

    Please help further..
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  2. #2
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    Re: Ratio and Proportion II

    notice that it is of the form A^2-B^2, you should try manipulating using the following formula, A^2-B^2=(A+B)(A-B)
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  3. #3
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    Re: Ratio and Proportion II

    If u noticed that I have already done..... if u can do it further than please let me know..
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  4. #4
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    Re: Ratio and Proportion II

    I have for k=1,2,3... where is a term of some infinite sequence { }

    Some manipulation:



    Is there anything I can do with this now?



    Is it legal to multiply the sums like this?

    The second factor looks like a geometric series and I should be able to get the sum of the terms equal to some constant A (if series converges).

    (for each k)



    Does that seem
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  5. #5
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    Re: Ratio and Proportion II

    Please recheck there is something amiss. Notice the powers of variables on both the sides??
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