. Determine the radius of convergence of the series 1 anz" when: (a) a₁ = (log n)² (b) an = n! (c) an = +3m

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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16. Determine the radius of convergence of the series an" when:
(a) an = (logn)²
(b) an = n!
n=1
(c) an = 4 +3m
(d) a₁ = (n!)³/(3n)!
[Hint: Use Stirling's formula, which says that
n!~ene" for some e > 0..]
(e) Find the radius of convergence of the hypergeometric series
F(a, 3₁ %; z) = 1 + a(a + 1) ... (a+n− 1)3(3+1) ··· (3 + n − 1) ¸n
n!y(y + 1) (y + n − 1)
n=1
Here a, 3 € C and y# 0,-1, -2,....
Transcribed Image Text:16. Determine the radius of convergence of the series an" when: (a) an = (logn)² (b) an = n! n=1 (c) an = 4 +3m (d) a₁ = (n!)³/(3n)! [Hint: Use Stirling's formula, which says that n!~ene" for some e > 0..] (e) Find the radius of convergence of the hypergeometric series F(a, 3₁ %; z) = 1 + a(a + 1) ... (a+n− 1)3(3+1) ··· (3 + n − 1) ¸n n!y(y + 1) (y + n − 1) n=1 Here a, 3 € C and y# 0,-1, -2,....
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