Solution Found!
Show that log n! is greater than (n log n)/4 for n > 4.
Chapter 2, Problem 73E(choose chapter or problem)
Show that \(\log n !\) is greater than \((n \log n) / 4\) for \(n>4\). [Hint: Begin with the inequality \(n !>n(n-1)(n-2) \cdots n / 2 .]\)
Let \(f(x)\) and \(g(x)\) be functions from the set of real numbers to the set of real numbers. We say that the functions \(f\) and \(g\) are asymptotic and write \(f(x) \sim g(x)\) if \(\lim _{x \rightarrow \infty} f(x) / g(x)=1\)
Equation Transcription:
· · · .]
Text Transcription:
(n log n)/4
n > 4
n! > n(n − 1)(n − 2) dot n/2.]
f(x)
g(x)
f
g
f (x) ∼ g(x)
Lim_x right arrow infinity f (x)/g(x) = 1
Questions & Answers
QUESTION:
Show that \(\log n !\) is greater than \((n \log n) / 4\) for \(n>4\). [Hint: Begin with the inequality \(n !>n(n-1)(n-2) \cdots n / 2 .]\)
Let \(f(x)\) and \(g(x)\) be functions from the set of real numbers to the set of real numbers. We say that the functions \(f\) and \(g\) are asymptotic and write \(f(x) \sim g(x)\) if \(\lim _{x \rightarrow \infty} f(x) / g(x)=1\)
Equation Transcription:
· · · .]
Text Transcription:
(n log n)/4
n > 4
n! > n(n − 1)(n − 2) dot n/2.]
f(x)
g(x)
f
g
f (x) ∼ g(x)
Lim_x right arrow infinity f (x)/g(x) = 1
ANSWER:
SOLUTION
Step 1
In this problem, we have to show that for .