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Thread: Induction Proof

  1. #1
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    Induction Proof

    The Basis is easy, my algebra sucks, can someone please help me with the inductive step? Even just a nice hint or start would be great.

    Thanks in advance.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by shawn View Post
    The Basis is easy, my algebra sucks, can someone please help me with the inductive step? Even just a nice hint or start would be great.

    Thanks in advance.
    so your base case is for n = 2.

    you want to show P(2) holds.

    then assume P(n) holds for some n

    then use that to show P(n + 1) holds.

    to start you off.

    Let $\displaystyle P(n)$: "$\displaystyle 3^n + 4^n \le 5^n$ for all $\displaystyle n \in \mathbb{N},~n \ge 2$"

    So, $\displaystyle P(2)$: $\displaystyle 3^2 + 4^2 = 9 + 16 = 25 \le 5^2$

    so, $\displaystyle P(2)$ holds.

    Assume $\displaystyle P(n)$ holds for some $\displaystyle n \ge 2$, we show $\displaystyle P(n + 1)$

    now continue
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