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Page 3 3. For |2 <1, 1+z+z²+... 2 Using this expansion, by matching terms show that if f(2)==0a, 2³, and f(z) g(z) 1-z Then the McLaurin expansion for g is no bnz", where bn ==0aj, 4. Deduce the McLaurin expansion of G(z) using the result of Step 3 and your knowledge of the series expansion of familiar functions. The co- efficients of the McLaurin expansion are the values of pn 5. Also deduce the result that if the number of hats is very large, then the probability no one gets his own hat is approximately e-1. = of 3 ZOOM

Page 3 3. For |2 <1, 1+z+z²+... 2 Using this expansion, by matching terms show that if f(2)==0a, 2³, and f(z) g(z) 1-z Then the McLaurin expansion for g is no bnz", where bn ==0aj, 4. Deduce the McLaurin expansion of G(z) using the result of Step 3 and your knowledge of the series expansion of familiar functions. The co- efficients of the McLaurin expansion are the values of pn 5. Also deduce the result that if the number of hats is very large, then the probability no one gets his own hat is approximately e-1. = of 3 ZOOM

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 56EQ
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3. For |2 <1, 3 1+z+z²+ = 2 2 Using this expansion, by matching terms show that if f(2)==0;z³, and f(z) g(z) = 1-z Then the McLaurin expansion for g is no bnz", where bn = ₁=0aj, 4. Deduce the McLaurin expansion of G(z) using the result of Step 3 and your knowledge of the series expansion of familiar functions. The co- efficients of the McLaurin expansion are the values of Pn. 5. Also deduce the result that if the number of hats is very large, then the probability no one gets his own hat is approximately e-1. Page 1 of 3 ZOOM
Transcribed Image Text:3. For |2 <1, 3 1+z+z²+ = 2 2 Using this expansion, by matching terms show that if f(2)==0;z³, and f(z) g(z) = 1-z Then the McLaurin expansion for g is no bnz", where bn = ₁=0aj, 4. Deduce the McLaurin expansion of G(z) using the result of Step 3 and your knowledge of the series expansion of familiar functions. The co- efficients of the McLaurin expansion are the values of Pn. 5. Also deduce the result that if the number of hats is very large, then the probability no one gets his own hat is approximately e-1. Page 1 of 3 ZOOM
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