To determine To prove: That n 2 − n + 2 is a solution to the recurrence relation r n = r n − 1 + 2 ( n − 1 ) for n ≥ 2 with the initial condition r 1 = 2 . Explanation Proof: Prove by using mathematical induction as follows. It is enough to prove that r n = n 2 − n + 2 for n ≥ 2 with the initial condition r 1 = 2 . Basis of induction: Since r n = n 2 − n + 2 , so r 1 = 1 2 − 1 + 2 = 2 Thus, r n = n 2 − n + 2 is true for n = 1 . Inductive hypothesis: Assume r n = n 2 − n + 2 is true for n = k . Thus r k = k 2 − k + 2 … ( i ) Inductive step: Since r n = r n − 1 + 2 ( n − 1 ) , so r k + 1 = k 2

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ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Chapter 9.2, Problem 1E

To determine

To prove: That n2−n+2 is a solution to the recurrence relation rn=rn−1+2(n−1) for n≥2 with the initial condition r1=2.

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Chapter 9.1, Problem 38E

Chapter 9.2, Problem 2E

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