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Math Help - prove by mathematical introdution that

  1. #1
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    prove by mathematical introdution that

    prove by mathematical induction that: -

    1^4 + 2^4 + 3^4 + .... + n^4 = 6n^5 + 15n^4 + 10n^3 - n
    30

    Hint : ( Expand 6(n-1)^5 +15(n-1)^4 +10(n-1)^3 -(n-1) as a polynomial in n.)


    please help me...
    give me some example to solve this problem
    i just don't want the answer buy the work outs
    thank you
    Last edited by 425611; August 19th 2008 at 09:14 PM.
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  2. #2
    Member
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    Hello,

    What we know (from the induction hypothsesis):
    1^4 + 2^4 + 3^4 + .... + (n-1)^4 = (1/30)(6(n-1)^5 + 15(n-1)^4 + 10(n-1)^3 - (n-1)).

    What we want to prove:
    1^4 + 2^4 + 3^4 + .... + n^4 = (1/30)(6n^5 + 15n^4 + 10n^3 - n)

    So, all we have to prove is:
    -n^4=(1/30)(6(n-1)^5 + 15(n-1)^4 + 10(n-1)^3 - (n-1))-(1/30)(6n^5 + 15n^4 + 10n^3 - n).

    Bye
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