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Math Help - mathematical induction inequalities

  1. #1
    Senior Member polymerase's Avatar
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    Question mathematical induction inequalities

    how do i show that the statement hold for every positive integer n using induction?

    (1+ n)2 ≥ 3n + 1
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  2. #2
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    Quote Originally Posted by polymerase View Post
    how do i show that the statement hold for every positive integer n using induction?

    (1+ n)2 ≥ 3n + 1
    I assume you mean,
    (n+1)^2 \geq 3n+1

    It is true for n=1.
    Assume it is true for n=k that is,
    (k+1)^2 \geq 3k+1

    Then,
    (k+2)^2 = k^2+4k+4 = (k^2+2k+1)+(2k+2)\geq 3k+1 + 3 = 3(k+1)+1
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