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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.

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.

Algebra & Trigonometry with Analytic Geometry
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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3. Let n Є N \ {0}. Describe the largest set of values n for which you think 2n < 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).
Transcribed Image Text:3. Let n Є N \ {0}. Describe the largest set of values n for which you think 2n < 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).
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