Science:Math Exam Resources/Courses/MATH220/April 2011/Question 07 (c)/Solution 1

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We will prove this statement by induction on .

First, for . By definition of the sequence we have that

which proves the first step of our induction.

Let us now assume that the statement is true for all values of up to and let us show that the statement holds for .

In part (b) we showed that

hence we can guarantee that

and so, we have that

which concludes our proof.