# Use mathematical induction to prove...

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See attached file for full problem description.

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:

(1+x)<=(1+x)

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.

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