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Thread: [Discrete Math] Mathematical Induction

  1. #1
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    [Discrete Math] Mathematical Induction

    So I'm trying to prove that (n+1)/2 is the mean of the first n integers by math induction.

    I mainly need help setting it up. Would it be:

    (1+2+3+...+n)/n = (n+1)/2 ?
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  2. #2
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    Re: [Discrete Math] Mathematical Induction

    Yes, that's the statement you have to prove.
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  3. #3
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    Re: [Discrete Math] Mathematical Induction

    [Discrete Math] Mathematical Induction-mean.jpg

    Is it like this?
    Attached Thumbnails Attached Thumbnails [Discrete Math] Mathematical Induction-meanproof.jpg  
    Last edited by MrJank; Nov 15th 2018 at 04:31 PM.
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  4. #4
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    Re: [Discrete Math] Mathematical Induction

    Good attempt, but not quite.

    After your assumption that the statement is true for i, you need to prove it is true for (i+1).

    That is, you need to prove that $\displaystyle \frac{1+2+3+...+i+(i+1)}{i+1} = \frac{(i+1)+1}{2}$

    Have another go.

    Also, another point:
    With a proof like this, you should
    (a) Work with the LHS only and turn it into the RHS.
    OR (b) Work with the RHS only and turn it into the RHS.
    OR (c) Work with the LHS as far as you can. Then work with the RHS as far as you can. Hopefully they will then be equal.

    You can't work with both at the same time (as you've done) because you don't know at the beginning (yet) that the LHS=RHS.
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