This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 153
Selected Solutions for §11.7 I’m doing this section diﬀerently; instead of giving a select few answers, I’m
going to give all answers along with the test used to derive that answer. Feel
free to ask for clariﬁcation on any problem.
CT = Comparison Test, LCT = Limit Comparison Test, IT = Integral Test,
DT = Divergence Test, AST = Alternating Series Test, RaT = Ratio Test,
RoT = Root Test. Converges; CT/LCT with
Converges; RoT
Diverges; DT or AST
Converges; AST
Converges; RaT/RoT 1
3n Exercise
Exercise
Exercise
Exercise
Exercise 1:
2:
3:
4:
5: Exercise
Exercise
Exercise
Exercise
Exercise 1
6: Diverges; LCT with n
7: Diverges; IT
8: Diverges; RaT
9: Converges; IT or RaT/RoT
10: Converges; IT or RaT/RoT Exercise
Exercise
Exercise
Exercise
Exercise 11:
13:
14:
15:
16: Converges; AST
Converges; RaT
Converges; CT with
Converges; RaT
Diverges; LCT with Exercise
Exercise
Exercise
Exercise
Exercise 17:
18:
19:
20:
21: Diverges; DT or AST
Converges; AST
Converges; AST
Converges; RaT/RoT
Converges; RoT Exercise
Exercise
Exercise
Exercise 22:
24:
25:
26: Converges; CT/LCT with
Diverges; DT
Converges; RaT
Converges; RaT/RoT 1
2n (ﬁrst take absolute value) 1
n 1 1
n2 2 Exercise 27: Converges; CT with
Exercise
Exercise
Exercise
Exercise
Exercise 28:
30:
31:
32:
33: k ln k
k3 = lnk
k2 followed by IT on e
Converges; CT with n2 or LCT with
Converges; AST
n
Diverges; CT with 254n
·
Diverges; DT or RoT
1
Diverges; LCT with √n Exercise 34: Diverges; CT/LCT with 21
n
Exercise 35: Converges; RoT (lim = 1 )
e
Exercise 37: Converges; RoT 1
n2 ln k
k2 ...
View
Full
Document
This note was uploaded on 07/26/2011 for the course MATH 153 taught by Professor Rempe during the Spring '08 term at Ohio State.
 Spring '08
 REMPE
 Math

Click to edit the document details