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Math Help - Factoring

  1. #1
    ilj
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    Factoring

    Hi all,

    I am looking at mathamatical induction and seem to be stuck on why the answer to a factoring step is correct.

    r(r+1)+2(r+1) factored by r+1 gives (r+1)(r+2)

    2(r+1) factored by r+1 to give (r+2) is clear but I cannot fathom r(r+1) factored by r+1 gives r+1.

    Here is the link to the page on induction and is below line 1
    Mathematical induction - Topics in precalculus

    This is my first post here so please be gentle.
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  2. #2
    Senior Member BAdhi's Avatar
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    Quote Originally Posted by ilj View Post
    2(r+1) factored by r+1 to give (r+2) is clear
    can you elaborate this?
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  3. #3
    ilj
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    Ok,

    2(r+1) simplified gives 2r+2

    2r+2/r+1=r+2

    Hmm that doesn't look correct.

    Am I on the wrong track completly?

    This is the progression I am stuck on.

    1+2+3+....+k+(k+1) = k(k+1)/2 +(k+1)

    =k(k+1)+2(k+1)/2

    on adding these fractions

    =(k+1)(k+2)/2
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  4. #4
    Senior Member BAdhi's Avatar
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    for easiness, take (k+1) as 'a'

    then [k(k+1)+2(k+1)]/2 will be [ka+2a]/2

    since a is common, [ka+2a]/2=a[k+2]/2 which is (k+1)(k+2)/2
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  5. #5
    ilj
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    That is a very good explanation, thank you very much, I will use that method again.
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  6. #6
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    Are you asking why r(r + 1) + 2(r + 1) = (r + 1)(r + 2)? If so, it should be obvious that there is a common factor of (r + 1)...
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  7. #7
    ilj
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    Yes I did know that but didn't know how to use factoring, that was my issue. After 30 or so years you tend to forget a few things.
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