b. 6. Use the limit comparison test to determine the convergence of the series. 2 3"-5 a. b. a. b. C. d. 1 n=1 4√n-1 7. For each of the series below, use at least two of the tests to determine the convergence of the series. Each test should be used at least once. Choose from: nth-term test, p-series test, integral test, limit comparison test, geometric series test, telescoping series test, direct comparison test. Clearly indicate which tests you are using. (-3)* 1 ¹3n²-2n-15 a. n=1 b. n=1 C. n=1 WW n=1 n=1 n=1 n=1 tan n=1 Zn=1 n 1 ¹3" +2 e. Yo f. E=1 n+6" 1 g. Σ=1 1 n¹+n 00 n=0 n 2n +3 n=1 2 n + n-1 n²√n n+4" 500 (-1)+1√√n Σn=1 3√n (-1)^n² n² +1 сOS NÃ d. Σ(-1)"e-n² e. Σ(-1)"+¹ arctan n C. f. Ex-1(-1)" sin (7) n=1 n=1n(n² +1) 8. Determine the convergence or divergence of the series. If the series converges, does it converge absolutely or conditionally? h. i. 1 j. k. n=0 n=4 i. 1 1 n+1 n+2, 3 n=1 n(n+3) 1.00 n=1 k. Zk=1 m. Σ=1 n 1 n. 1 sin / 100 (-1)"+¹ In(n+1) n+1 n=1 j. Ŝ (-1)"+¹ √n n=1 n+2 (2k-1) (k²-1) (k+1)(k²+4) e1/n n=2 1. Ž (-1)" Inn COSNT n=0 n+1 m. E-1(-1)-12/n 00 n. Ln=1 (-1)^nn n!
b. 6. Use the limit comparison test to determine the convergence of the series. 2 3"-5 a. b. a. b. C. d. 1 n=1 4√n-1 7. For each of the series below, use at least two of the tests to determine the convergence of the series. Each test should be used at least once. Choose from: nth-term test, p-series test, integral test, limit comparison test, geometric series test, telescoping series test, direct comparison test. Clearly indicate which tests you are using. (-3)* 1 ¹3n²-2n-15 a. n=1 b. n=1 C. n=1 WW n=1 n=1 n=1 n=1 tan n=1 Zn=1 n 1 ¹3" +2 e. Yo f. E=1 n+6" 1 g. Σ=1 1 n¹+n 00 n=0 n 2n +3 n=1 2 n + n-1 n²√n n+4" 500 (-1)+1√√n Σn=1 3√n (-1)^n² n² +1 сOS NÃ d. Σ(-1)"e-n² e. Σ(-1)"+¹ arctan n C. f. Ex-1(-1)" sin (7) n=1 n=1n(n² +1) 8. Determine the convergence or divergence of the series. If the series converges, does it converge absolutely or conditionally? h. i. 1 j. k. n=0 n=4 i. 1 1 n+1 n+2, 3 n=1 n(n+3) 1.00 n=1 k. Zk=1 m. Σ=1 n 1 n. 1 sin / 100 (-1)"+¹ In(n+1) n+1 n=1 j. Ŝ (-1)"+¹ √n n=1 n+2 (2k-1) (k²-1) (k+1)(k²+4) e1/n n=2 1. Ž (-1)" Inn COSNT n=0 n+1 m. E-1(-1)-12/n 00 n. Ln=1 (-1)^nn n!
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Need help with Number 7 A to F if possible but if you can do A TO D too that's fine.
Transcribed Image Text:b.
a.
6.
Use the limit comparison test to determine the convergence of the series.
2
¹3"-5
b.
a.
b.
C.
d.
n=1
00
a.
b.
74√/1²-²
n=1
∞0
7. For each of the series below, use at least two of the tests to determine the convergence of the
series. Each test should be used at least once. Choose from: nth-term test, p-series test,
integral test, limit comparison test, geometric series test, telescoping series test, direct
comparison test. Clearly indicate which tests you are using.
Σ(-3)
n=0
n=1
L√n
n
18 IMS IM8
n=1
00
tan
e. Σ=1
f. Σn=1
g. Σ=1
n=1
1
¹3" +2
n=1 n² +
∞
n
'2n + 3
00
Ic
n=1
n
∞
c. Σ=1
n=0
n
² + 1)²
n-1
n² √√n
n+4n
n=1
n+6n
1
1+=
n n
COSNT
d. Σ(-1)"e-n²
(−1)n+1 √n
Vn
C.
\n+
e. Σ(-1)"+¹ arctan n
f. Σ=1(-1)" sin
1
n=n(n² +1)
h.
i.
j.
k.
8. Determine the convergence or divergence of the series. If the series converges, does it
converge absolutely or conditionally?
(−1)″ n²
n² +1
00
i.
j.
n=4
Σ
n=1\n+1
00
n=1
I.
I.E=1
m. 2n=1
Σ=
1
3n²-2n-15
100
n. Σn=₁ sin
WW
1
n=1
3
n(n+3)
n=0
(2k-1)(k²-1)
(k+1)(k²+4)
e1/n
n
(−1)n+¹
n=1
k. † (-1)"
In n
n=2
1
n+2
1
n
n+¹ In(n+1)
·
COSNT
n+1
n+1
(−1)¹+¹ √√n
n+2
m. Σã=₁(−1)n-¹e²/n
n. Σ=1
(-1)^nn
n!
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