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Math Help - Mathematical inductions

  1. #1
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    Mathematical inductions

    Hi

    i have a couple of exercises in math and i am not sure if i solved them right. Can someone please tell me what the solutions are?

    First principal mathematical induction

    1/(1*3)+ 1/(3*5)+...+1/(2n-1)(2n+1)=n/2n+1


    Second principle of mathematical induction

    n!<n^n for n>1

    thank you 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 tironci View Post
    Hi

    i have a couple of exercises in math and i am not sure if i solved them right. Can someone please tell me what the solutions are?

    First principal mathematical induction

    1/(1*3)+ 1/(3*5)+...+1/(2n-1)(2n+1)=n/2n+1
    Let P(n): " \frac 1{1 \cdot 3} + \frac 1{3 \cdot 5} + \cdots + \frac 1{(2n - 1)(2n + 1)} = \frac n{2n + 1}" for all n \in \mathbb{N} (i take \mathbb{N} to be the positive integers here)

    Step 1: Show that P(1) is true.

    Step 2: Assume P(n) is true and show that this implies P(n + 1) is true

    Then the claim will hold for all n \in \mathbb{N} by mathematical induction


    Second principle of mathematical induction

    n!<n^n for n>1

    thank you in advance
    how did you define the second principle of induction. in a class i am taking we did three forms, and i know of another from a previous class. i want to make sure we are on the same page.
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  3. #3
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    in class we did only the first principle of induction and the second principle of induction which is also called "Strong Induction"

    Thank you for your help
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