Prove each of the following statements true for any positive integer n using induction or strong induction: (a) 12 + 22 + 32 + · · · + n2 = (n(n+1)(2n+1))/6 (b) 2n + (−1)n+1 is divisible by 3. (c)Let an be the sequence defined by a1 = 1, a2 = 8, an = an−1 + 2an−2 for n ≥ 3. Prove that an = 3 × 2n−1 + 2(−1)n for all n.

Prove each of the following statements true for any positive integer n using induction or strong induction: (a) 12 + 22 + 32 + · · · + n2 = (n(n+1)(2n+1))/6 (b) 2n + (−1)n+1 is divisible by 3. (c)Let an be the sequence defined by a1 = 1, a2 = 8, an = an−1 + 2an−2 for n ≥ 3. Prove that an = 3 × 2n−1 + 2(−1)n for all n.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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