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    Please provide proof along with explanation.

    For integers n>= 1 and for all real numbers x>=-1, use mathematical induction to prove that 1 + nx =< (1 + x)^n.

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    Solution Preview

    We first consider the case of n=1:
    That is obviously true.

    Now let's assume that for some real n=k (k>=1) the inequality holds, i.e.
    (1+kx)<=(1+x)^k ...

    Solution Summary

    Mathematical induction is used to provide a proof.