k=1 8 27. Σ k=1 sin k k2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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help with 27, using the integral test to determine wetther the followling converge or diverge, only use integral test don't try to use other test, if it is inconclusive please explain why. please do it step by step on paper. Thanks.

h series converge. By Property 2 of Theorem 10.13, we
e S = 10 - =
49
CK CHECK 5 For a series with positive terms, explain wh
Sn} is an increasing sequence.
ermine whether a
ive terms decrease
using an example.
hether a series diverges?
converge? For what
P
converge (initial
diverge?
for a series with posi-
8
k
24/14
25. Σ
8
27. Σ
k=1
29. Σ
a.
sin k
k²
29-34. p-series Determine the conve
following series.
k=1 k ¹0
32. Σ 2k-3/2
k=1
Σ
26. k In k
k
(k² +
28.
Σ
30.
ke
k"
k=2
1
33. Σ √k
k=1
T 35-42. Remainders and estimates
series.
Find an upper bound for the rem
ad
how many terms are needed
Transcribed Image Text:h series converge. By Property 2 of Theorem 10.13, we e S = 10 - = 49 CK CHECK 5 For a series with positive terms, explain wh Sn} is an increasing sequence. ermine whether a ive terms decrease using an example. hether a series diverges? converge? For what P converge (initial diverge? for a series with posi- 8 k 24/14 25. Σ 8 27. Σ k=1 29. Σ a. sin k k² 29-34. p-series Determine the conve following series. k=1 k ¹0 32. Σ 2k-3/2 k=1 Σ 26. k In k k (k² + 28. Σ 30. ke k" k=2 1 33. Σ √k k=1 T 35-42. Remainders and estimates series. Find an upper bound for the rem ad how many terms are needed
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