Determine whether the series 8 n=0 C|N OB. 2 converges or diverges. If it converges, find its sum. Select the correct choice below and, if necessary, fill in the answer box within your choice. n 2 OA. The series converges because lim e k∞n=0 ... k fails to exist. The series converges because it is a geometric series with |r|<1. The sum of the series is (Type an exact answer.) O c. The series diverges because it is a geometric series with r≥ 1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Determine whether the series
8
n=0
B.
e
n
2
Select the correct choice below and, if necessary, fill in the answer box within your choice.
O E.
converges or diverges. If it converges, find its sum.
n
k
O A. The series converges because lim Σ 2 fails to exist.
e
k→∞n n=0
The series converges because it is a geometric series with |r| < 1. The sum of the series is
(Type an exact answer.)
C. The series diverges because it is a geometric series with |r| ≥ 1.
D. The series diverges because lim e
n→∞
n
The series converges because lim e
n→∞
(Type an exact answer.)
#0 or fails to exist.
n
2
= 0. The sum of the series is
Transcribed Image Text:Determine whether the series 8 n=0 B. e n 2 Select the correct choice below and, if necessary, fill in the answer box within your choice. O E. converges or diverges. If it converges, find its sum. n k O A. The series converges because lim Σ 2 fails to exist. e k→∞n n=0 The series converges because it is a geometric series with |r| < 1. The sum of the series is (Type an exact answer.) C. The series diverges because it is a geometric series with |r| ≥ 1. D. The series diverges because lim e n→∞ n The series converges because lim e n→∞ (Type an exact answer.) #0 or fails to exist. n 2 = 0. The sum of the series is
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