Discrete Math Define 0! = 1. For any positive integer n, define n! = n·(n−1)!. For example, 6! = 6×5×4×3×2×1 = 720. Use induction to show that 4^n/(n + 1) < (2n)!/(n!)^2 for all integer n ≥ 2.

Discrete Math Define 0! = 1. For any positive integer n, define n! = n·(n−1)!. For example, 6! = 6×5×4×3×2×1 = 720. Use induction to show that 4^n/(n + 1) < (2n)!/(n!)^2 for all integer n ≥ 2.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.4: Mathematical Induction

Problem 10E

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Question

Discrete Math

Define 0! = 1. For any positive integer n, define n! = n·(n−1)!. For example, 6! = 6×5×4×3×2×1 = 720. Use induction to show that 4^n/(n + 1) < (2n)!/(n!)^2 for all integer n ≥ 2.

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