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Math Help - Inequality!!

  1. #1
    MHF Contributor harish21's Avatar
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    Inequality!!

    If x1, x2,….., xn are positive numbers and n is a natural number, how do you prove that
    (1+ x1)(1+ x2)…..(1+ xn) >= 1+ x1+ x2+…..+ xn


    The only thing I can think of here is that ∏(1+xi) - ∑ xi >=1 , where i goes from 1 to n
    Is induction required here?
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    Quote Originally Posted by harish21 View Post
    If x1, x2,.., xn are positive numbers and n is a natural number, how do you prove that
    (1+ x1)(1+ x2)..(1+ xn) >= 1+ x1+ x2+..+ xn


    The only thing I can think of here is that ∏(1+xi) - ∑ xi >=1 , where i goes from 1 to n
    Is induction required here?
    Yes induction is required :

    for n=1 we have: 1+x_{1}\geq 1+x_{1}

    Now assume the inequality to hold for n=k and then prove it holds for n=k+1
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