Exercise 6.6. Let the inductive set be equal to all natural numbers, N.Prove the following propositions.(a) Vn, 2n ≥ 1+ n.(b) Vn, 4¹ – 1 is divisible by 3.(c) Vn, 3n ≥ 1+2″.(d) Vn, 2¹ +2²+ ... + 2n = 2n+1 − 2.

Answered: Exercise 6.6. Let the inductive set be…

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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Exercise 6.6. Let the inductive set be equal to all natural numbers, N. Prove the following propositions. (a) Vn, 2n ≥ 1 + n. (b) Vn, 4 - 1 is divisible by 3. (c) Vn, 3n 1+2n. (d) Vn, 2¹ +2²+...+2n = 2n+1 -2.