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Math Help - induction inequalities P3

  1. #1
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    induction inequalities P3

    Prove using the principle of mathematical induction that

    (1+x)^n> (or equal to) 1+nx, n=1,2,3...

    thank you !
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  2. #2
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  3. #3
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    Quote Originally Posted by christina View Post
    Prove using the principle of mathematical induction that

    (1+x)^n> (or equal to) 1+nx, n=1,2,3...

    thank you !
    This is very straightforward.

    If (1+x)^n\ \ge\ 1+nx ......(1)

    then (1+x)^{n+1}\ must\ be\ \ge\ 1+(n+1)x ....... (2)

    Try to prove this using (1)
    as this means (1) being true for some k causes (1) to be true for all n >k.

    (1+x)^k(1+x)\ \ge\ (1+kx)(1+x) ?

    (1+x)^{k+1}\ \ge\ 1+kx+x+kx^2 ?

    (1+x)^{k+1}\ \ge\ 1+(k+1)x+kx^2 which is > 1+(k+1)x
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