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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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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