   Chapter 11.4, Problem 46ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Let n be a variable that takes positive integer values.a. Use Example 11.4.6 to show that log 2 ( n ! ) is O ( n   log 2 n ) .b. Show that n n ≤ ( n ! ) 2 for every integer n ≥ 1 .c. Use part (b) to show that log 2 ( n ! ) is Ω ( n   log 2   n ) .d. Use parts (a) and (c) to find an order for log 2 ( n ! ) .

To determine

(a)

To prove:

Show that n! is O(nn).

Explanation

Given information:

Let n be a variable that takes positive values.

PROOF:

n!=1234...n                                               1234...n=n!

nnnn...nn repetitions                    in for

To determine

(b)

Use part (a) to show that log2(n!) is O(n log2 n).

To determine

(c)

Show that nn(n!)2 for all positive integers n2.

To determine

(d)

Use part (c) to show that log2(n!) is Ω(n log2 n).

To determine

(e)

Use part (b) and (d) to find an order for log2(n!).

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