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Math Help - Proof by induction?

  1. #1
    chixor1
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    Question Proof by induction?

    Im struggling on a problem ive been given in class and was wondering if anyone could point me in the right direction for the solution?

    The question is:

    Prove that n^2>=2n+3 for n>=3

    Am i correct in assuming this is proof by induction?
    So would I then do n=k
    so k^2>=2k+3

    Then do I do n=k+1??
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  2. #2
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    Quote Originally Posted by chixor1 View Post
    Im struggling on a problem ive been given in class and was wondering if anyone could point me in the right direction for the solution?

    The question is:

    Prove that n^2>=2n+3 for n>=3
    Is it true for n=3. Indeed.

    k^2>=2k+3

    Add 2k to both sides,

    k^2+2k>=2k+2k+3

    Add 1 to both sides,

    k^2+2k+1>=2k+2k+3+1=(2k+2)+(2k+2)>=(2k+2)+3=2(k+1) +3
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  3. #3
    Newbie slobone's Avatar
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    Proof by induction always has two parts.

    Base step. Show that the statement is true for some minimal integer n. In this case, you want n = 3 because you're not interested in any integer lower than that.

    So in the base step you need to show that 3^2 >= 2(3) + 3.

    (Base step is usually the easy part.)

    Inductive step. Here you need to show that if the statement is true for n, then it's also true for n + 1.

    So you can make the assumption that for some arbitrary given integer n, it has already been shown that n^2 >= 2n + 3.

    You can use this to show that it must follow that (n + 1)^2 >= 2(n + 1) + 3. I would start by simplifying the equation, then compare what you get with what you already know.
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