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Math Help - prove by induction algebra help!

  1. #1
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    prove by induction algebra help!

    a sequece of integers x1,x2...xk..is defined recursively as follows:
    x1=1 and xk+1 =xk/xk+2 for kis greater then or equal to 1
    calculate x2,x3 and x4...i got
    k=1:x1+1 =x1/x1+2=1/1+2=3=x^2
    k=2:x2+1 =x2/x2+2=3/3+2=3=x^3
    k=3:x3+1 =x3/x3+2=3/3+3=4=x^
    is this right and another question using the info in the fisrt part how do i find and prove by induction a formula for the nth term xn in terms of n for all n is greater than or equal to 1,calcilate x10.
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  2. #2
    Super Member Bacterius's Avatar
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    Re: prove by induction algebra help!

    Wait do you mean x_{k + 1} = \frac{x_k}{x_{k + 2}} or x_{k + 1} = \frac{x_k}{x_k} + 2? Can you clarify please and clean up your question as it's very ambiguous right now
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  3. #3
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    Re: prove by induction algebra help!

    sorry its the first one you wrote..i didnt how to type it like you did so its a little messy sorry
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: prove by induction algebra help!

    Quote Originally Posted by university View Post
    k=1:x1+1 =x1/x1+2=1/1+2=3=x^2
    k=2:x2+1 =x2/x2+2=3/3+2=3=x^3
    k=3:x3+1 =x3/x3+2=3/3+3=4=x^
    This is also not clear, if k=1 then:
    x_2=\frac{x_1}{x_3} \Leftrightarrow x_2=\frac{1}{x_3}

    Do you mean something like this? ...
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  5. #5
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    Re: prove by induction algebra help!

    well i just subbed in the numbers everwhere there was xk
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  6. #6
    Super Member Bacterius's Avatar
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    Re: prove by induction algebra help!

    well i just subbed in the numbers everwhere there was xk
    x_{k + 1} \ne x_k + 1
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