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Math Help - Mathematical induction

  1. #1
    Junior Member BERMES39's Avatar
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    Mathematical induction

    Can someone show me how to do the following proof using mathematical induction:

    Assuming that the triangle inequality |a+b| \leq |a|+|b| holds for any two numbers a and b, show that


    | x_{1}+x_{2}+...+x_{n}| \leq | x_{1}|+| x_{2}|+...+| x_{n}|

    for any n numbers.

    Thank you.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Mathematical induction

    Hint: In the induction step consider a=x_1+\ldots+x_n and b=x_{n+1} .
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  3. #3
    Junior Member BERMES39's Avatar
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    Re: Mathematical induction

    Thank you for the hint. Still, I will appreciate if someone gives me the full solution.
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  4. #4
    MHF Contributor
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    Re: Mathematical induction

    Quote Originally Posted by BERMES39 View Post
    Thank you for the hint. Still, I will appreciate if someone gives me the full solution.
    Wouldn't we all. Come on. Throw us a bone and prove that you can give it a go. Show us ANYTHING.
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