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Math Help - Prove

  1. #1
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    Prove

    Prove that (1+2+2^2+2^3+...+2^200)       \vdots 7

    note :there is +...+2^200 ,problem with latex
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  2. #2
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    Hello, beq!x !

    What does the \vdots mean? . . . "is divisible by" ?
    If so, I have a proof . . .


    Prove that: . 1+2+2^2+2^3+ \hdots +2^{200} .is divisible by 7.

    N \;=\;(1 + 2 + 2^2) + (2^3+2^4+2^5) + (2^6+2^7+2^8) + \cdots + (2^{198} + 2^{199} + 2^{200})

    . . =\;(1+2+4) + 2^3(1+2+4) + 2^6(1+2+4) + \cdots + 2^{198}(1+2+4)

    . . =\; \underbrace{7\left(1 + 2^3 + 2^6 + 2^9 + \cdots + 2^{198}\right)}_{\text{a multiple of 7}}


    Therefore, N is divisible by 7.

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  3. #3
    MHF Contributor chiph588@'s Avatar
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    The code for  2^{200} is 2^{200} and the is divisible symbol  \mid is /mid.
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