5. Show that another approximation for log n! for large n is log n!=nlog(n)-n by expanding the log into a sum over the log of each term in the n! product and then approximating the resulting sum by an integral. What is the percentage error between log n! and your result when n=10?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 19E
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5.
Show that another approximation for log n! for large n is log n!=nlog(n)-n by expanding the log into
a sum over the log of each term in the n! product and then approximating the resulting sum by an
integral. What is the percentage error between log n! and your result when n=10?
Transcribed Image Text:5. Show that another approximation for log n! for large n is log n!=nlog(n)-n by expanding the log into a sum over the log of each term in the n! product and then approximating the resulting sum by an integral. What is the percentage error between log n! and your result when n=10?
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