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Advanced Math

Consider the statement n2 + 1 ≥ 2n where n is an integer in [1, 4].

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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Question

Consider the statement n² + 1 ≥ 2ⁿ where n is an integer in [1, 4].

Is the correct proof of the given statement is "For n = 1, 1² + 1 = 2 ≥ 2 = 2¹; for n = 2, 2² + 1 = 5 ≥ 4 = 2²; for n = 3, 3² + 1 = 10 ≥ 8 = 2³; and for n = 4, 4² + 1 = 17 ≥ 16 = 2⁴."

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