Exercise 23.  Use induction to prove that    for all natural numbers n.

Solution 23.

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When is clearly true that .  

Suppose that, for some  ,  that    .  

Then, using the triangle inequality and our induction assumption,

        .

Thus the result is established by mathematical induction.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell