11. Series k=1 For each of the following sequences {a}, decide wether the series Σak is convergent or not. You must specify what test you use, and why this test applies. (a) ak = 2, (b) a = ²+2 3k 2k +1 (c) ak = (d) ak = (e) ak = (f) ak = (g) ak = (h) ak = (i) ak = k2 (k+1)³ sin k k² (-1) In(k+2) 3k+2. cos (km)k! 10k (3k)!(k+1)! (4k)!

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
11. Series
k=1
For each of the following sequences {a}, decide wether the series Σak is convergent or
not. You must specify what test you use, and why this test applies.
(a) ak = 2,
(b) a = ²+2
3k
2k +1
(c) ak =
(d) ak =
(e) ak =
(f) ak =
(g) ak =
(h) ak =
(i) ak =
k2
(k+1)³
sin k
k²
(-1)
In(k+2)
3k+2.
cos (km)k!
10%
(3k)!(k+1)!
(4k)!
Transcribed Image Text:11. Series k=1 For each of the following sequences {a}, decide wether the series Σak is convergent or not. You must specify what test you use, and why this test applies. (a) ak = 2, (b) a = ²+2 3k 2k +1 (c) ak = (d) ak = (e) ak = (f) ak = (g) ak = (h) ak = (i) ak = k2 (k+1)³ sin k k² (-1) In(k+2) 3k+2. cos (km)k! 10% (3k)!(k+1)! (4k)!
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