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Math Help - Pythagorean triple

  1. #1
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    Pythagorean triple

    prove algebraicly the sum of the reciprocals of 2 consecutive odd numbers always produces the leg of a pythagorem triple

    1/3+1/5=8/15
    8^2+15^2=17^2

    let 2n-1 and 2n+1 be the two odd natural numbers..

    1/(2n-1)+1/(2n+1)=(2n-1)+(2n+1)/(2n-1)(2n+1)
    =4n/4n^2 -4n+1

    thats as fathest as i can get
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by juanfe_zodiac View Post
    prove algebraicly the sum of the reciprocals of 2 consecutive odd numbers always produces the leg of a pythagorem triple

    1/3+1/5=8/15
    8^2+15^2=17^2

    let 2n-1 and 2n+1 be the two odd natural numbers..

    1/(2n-1)+1/(2n+1)=(2n-1)+(2n+1)/(2n-1)(2n+1)
    =4n/{4n^2 \color{red}-4n+1}

    thats as fathest as i can get
    The part in red is incorrect. (2x+1)(2x-1)=4x^2-1. So you should have \frac{4n}{4n^2-1}

    From here, I'm sure mathematical induction would be useful here to complete the proof.
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    The part in red is incorrect. (2x+1)(2x-1)=4x^2-1. So you should have \frac{4n}{4n^2-1}

    From here, I'm sure mathematical induction would be useful here to complete the proof.
    so thats the end of the question???
    because i put n=4 and i did get 17^2

    can you correct me please
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  4. #4
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    Quote Originally Posted by Chris L T521 View Post
    The part in red is incorrect. (2x+1)(2x-1)=4x^2-1. So you should have \frac{4n}{4n^2-1}

    From here, I'm sure mathematical induction would be useful here to complete the proof.
    still dont getting it...help plz
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