3. Let n Є 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).
3. Let n Є 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).
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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PLEASE HELP ME. kindly show all your work
3. Let n ∈ 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 log2 n).
THANK YOU
3OoyQaGwGPYnEumugVXv
![3. Let n Є 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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8c33328-8191-4f2d-a012-7fb5fe2f2da3%2F63b4f5ed-f564-4b71-910c-099a99c8da05%2F67ijb9e_processed.png&w=3840&q=75)
Transcribed Image Text:3. Let n Є 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).
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