MATH220 April 2011
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q2 • Q3 (a) • Q3 (b) • Q4 • Q5 • Q6 • Q7 (a) • Q7 (b) • Q7 (c) • Q8 • Q9 (a) • Q9 (b) • Q9 (c) • Q10 (a) • Q10 (b) •
Question 07 (c)
Let be a sequence defined by
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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.
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