Prologue: The series diverges otherwise. T = A. Σ (5 + n(7) ") " This series ? B. n Problem: Each of the series below can be compared to a series of the form T = C. This series ? T = n=1 D. r = n=1 72n 7 +229 This series ? oo √n +3 n² +7 8 WI $ This series ? ? 20²2 3n²+7n+ 5-3n gn+8+7n +7√ñ converges Hote: You ca diverges converges when -1 < converges when -1 r < < r < 1 1 and diverges when |r| > 1. This i diverges when r > 1. This is true regardless of the value of the constant p. When r = 1 the series is a p-series. It converges if p > 1 and and 3 edit on this problem. 00 n=1 7² In each case, determine the best value of r and decide whether the series converges. ne
Prologue: The series diverges otherwise. T = A. Σ (5 + n(7) ") " This series ? B. n Problem: Each of the series below can be compared to a series of the form T = C. This series ? T = n=1 D. r = n=1 72n 7 +229 This series ? oo √n +3 n² +7 8 WI $ This series ? ? 20²2 3n²+7n+ 5-3n gn+8+7n +7√ñ converges Hote: You ca diverges converges when -1 < converges when -1 r < < r < 1 1 and diverges when |r| > 1. This i diverges when r > 1. This is true regardless of the value of the constant p. When r = 1 the series is a p-series. It converges if p > 1 and and 3 edit on this problem. 00 n=1 7² In each case, determine the best value of r and decide whether the series converges. ne
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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Question
Transcribed Image Text:Prologue: The series
diverges otherwise.
A.
T =
Problem: Each of the series below can be compared to a series of the form
This series ?
r =
n=1
B. n"
C.
p =
00
n=1
This series?
r =
n=1
(5+ n(7)")-7
72n
7 +229
This series ?
00
2-1
√n +3
n² +7
D. 3n²+7n +5-3n
gn+8 + 7n+7√n
n=1
This series?
?
2/1
converges
Note: You can diverges
converges when -1 < r < 1 and diverges when || > 1. This is true regardless of the value of the constant p. When r = 1 the series is a p-series. It converges if p > 1 and
3
edit on this problem.
DO
n=1
In each case, determine the best value ofr and decide whether the series converges.
пр
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