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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Please help me with this question. I am having trouble understanding what to do. Please show all your work on paper
Course: Discrete mathematics for CS
Thank you
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5354a32c-ee07-469b-96d5-42a00c955615%2F7227a144-188e-4767-834b-8b8f4dcc5b59%2Fiax61w_processed.png&w=3840&q=75)
Transcribed Image Text: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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5354a32c-ee07-469b-96d5-42a00c955615%2F7227a144-188e-4767-834b-8b8f4dcc5b59%2Fhsgz8m8_processed.png&w=3840&q=75)
Transcribed Image Text:1. Prove that
Vk Є N, 1k + 2k +
...
+nk € (nk+1).
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