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Math Help - Prove Identities with Induction method

  1. #1
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    Prove Identities with Induction method

    Using the Induction method, prove for n-1

    1 + 3 + 9 + 27+ . . . 3n-1= (3n-1)/2

    1*20 + 2*21 + 3*22 + . . . + n*2n-1 = (n-1)2n + 1
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  2. #2
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    You copied the sums wrong.

    Take a look at the first few terms of each series and see whether they match the general formula that you provide at the end of each LHS ? Once you realize what the formulae are, prove them for n=1. Then assume that they are true for n-1 and add the general term for n to both sides of the equations. You should be able to get the rest of it by yourself.
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  3. #3
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    Hello, tammyr!

    C'mon . . . give us a break!
    Are we supposed to GUESS what you meant?


    Using the Induction method, prove for n-1 ?

    . . 1 + 3 + 9 + 27+ . . . 3n-1 = (3n-1)/2

    . . 1*20 + 2*21 + 3*22 + . . . + n*2n-1 = (n-1)2n + 1

    I'll take a guess at what you intended . . .


    1 + 3 + 9 + 27 + \hdots + 3^{n-1} \;=\;\dfrac{3^n-1}{2}


    1\cdot2^0 + 2\cdot2^1 + 3\cdot2^2 + \hdots + n\cdot2^{n-1} \;=\;(n-1)2^n + 1
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