We know the inequality when *n*=1 and when *n*=2 by the last exercise.
We will show that the truth of the inequality for *n*=*k* implies it for
*n*=*k*+1 when *k* is any integer. That will finish the proof. This
is an example of proof by induction.

By the triangle inequality (in the simplest case *n*=2),

So the inductive hypothesis that

implies

which is the triangle inequality for the case *n*= *k*+1.

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