The series converges when 0 1. This is true n=1 regardless of the value of the constant k. When r = 1 the series is a p-series. It converges if k < −1 and diverges otherwise. Each of the series below can be compared to a series of the form Σn. For n=1 each series determine the best value of r and decide whether the series converges. ∞ A. Σ (4+n(4)n)-6 n=1 r = 4^(-6) Β.Σ. n=1 r = C. ∞ n=" 36/3 P = 1 r = Ο.Σ n=1 NT 62n 3n +nº n.5 +4 n³ +4 4n² +6n +4-5n 6 Gn+10 +3n +4√n converges or diverges (c or d)? c converges or diverges (c or d)? d converges or diverges (c or d)? c 5 converges or diverges (c or d)? c
The series converges when 0 1. This is true n=1 regardless of the value of the constant k. When r = 1 the series is a p-series. It converges if k < −1 and diverges otherwise. Each of the series below can be compared to a series of the form Σn. For n=1 each series determine the best value of r and decide whether the series converges. ∞ A. Σ (4+n(4)n)-6 n=1 r = 4^(-6) Β.Σ. n=1 r = C. ∞ n=" 36/3 P = 1 r = Ο.Σ n=1 NT 62n 3n +nº n.5 +4 n³ +4 4n² +6n +4-5n 6 Gn+10 +3n +4√n converges or diverges (c or d)? c converges or diverges (c or d)? d converges or diverges (c or d)? c 5 converges or diverges (c or d)? c
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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Transcribed Image Text:The series
converges when 0 <r < 1 and diverges when r > 1. This is true
n=1
regardless of the value of the constant k. When r = 1 the series is a p-series. It converges if k < −1
and diverges otherwise. Each of the series below can be compared to a series of the form Σn. For
n=1
each series determine the best value of r and decide whether the series converges.
∞
A. Σ (4+n(4)n)-6
n=1
r = 4^(-6)
Β.Σ.
n=1
r =
C.
∞
n="
36/3
P = 1
r =
Ο.Σ
n=1
NT
62n
3n +nº
n.5 +4
n³ +4
4n² +6n +4-5n
6
Gn+10 +3n +4√n
converges or diverges (c or d)? c
converges or diverges (c or d)? d
converges or diverges (c or d)? c
5
converges or diverges (c or d)? c
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