The nth root of n! a. Show that lim,(2n7)/(2n) = 1 and hence, using Stirling's approximation (Chapter 8, Additional Exercise 52a), that Vn! - for large values of n. b. Test the approximation in part (a) for n = 40, 50, 60, ..., as far as your calculator will allow.
The nth root of n! a. Show that lim,(2n7)/(2n) = 1 and hence, using Stirling's approximation (Chapter 8, Additional Exercise 52a), that Vn! - for large values of n. b. Test the approximation in part (a) for n = 40, 50, 60, ..., as far as your calculator will allow.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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![The nth root of n!
a. Show that lim,(2n7)/(2n) = 1 and hence, using Stirling's
approximation (Chapter 8, Additional Exercise 52a), that
Vn! - for large values of n.
b. Test the approximation in part (a) for n = 40, 50, 60, ...,
as far as your calculator will allow.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29004117-aae5-49b2-8d4f-3404423eae8a%2F4863e7d0-9e95-4479-9c9a-0139a1d2f315%2Fgna5thk.jpeg&w=3840&q=75)
Transcribed Image Text:The nth root of n!
a. Show that lim,(2n7)/(2n) = 1 and hence, using Stirling's
approximation (Chapter 8, Additional Exercise 52a), that
Vn! - for large values of n.
b. Test the approximation in part (a) for n = 40, 50, 60, ...,
as far as your calculator will allow.
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