3. Let n = N \ {0}. Describe the largest set of values n for which you think 2" < n!. Use induction to prove that your description is correct. Here m! stands for m factorial, the product of first m positive integers. 4. Prove that log2 n! = O(n log n). 1. Prove that Vk Є N, 1k + 2k + ... +nk € (nk+1).

3. Let n = N \ {0}. Describe the largest set of values n for which you think 2" < n!. Use induction to prove that your description is correct. Here m! stands for m factorial, the product of first m positive integers. 4. Prove that log2 n! = O(n log n). 1. Prove that Vk Є N, 1k + 2k + ... +nk € (nk+1).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.5: The Binomial Theorem

Problem 35E

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