Nikita Sharma 2019W2 MATH 101 209
Assignment Homework 9 due 9/12/14 at 9pm
Note: if you need help with formatting your entry in interval
1. (1 point) notation please click here.
Given: Correct Answers:
40
An = n • (0.5,infinity)
4
Determine:
(a) whether {An }is convergent.
If convergent, enter the limit of convergence. If not, enter div . 5. (1 point) Determine whether the series is convergent or
divergent. If convergent, find the sum; if divergent, enter div .
∞
(b) whether ∑ An is convergent.
∞
n=1 3
Correct Answers: ∑ sin(6n) −
n=1 n
• 0
• 13.3333333333333
Answer:
2. (1 point) Correct Answers:
Given: • div
1
An = 0.96
n
Determine:
6. (1 point)
(a) whether {An }is convergent.
If the following series converges, compute its sum. If it di-
If convergent, enter the limit of convergence. If not, enter div .
verges to infinity, state your answer as inf . If it diverges to
∞ negative infinity, state your answer as -inf . If it diverges with-
(b) whether ∑ An is convergent. out being infinity or negative infinity, state your answer as div .
n=1
Correct Answers:
∞
• 0
• div ∑ (e−3n − e−3(n+1) )
n=1
3. (1 point) Let
5n
an = .
4n + 11
For the following answer blanks, decide whether the given se- Correct Answers:
quence or series is convergent or divergent. If convergent, enter • 0.0497870683678639
the limit (for a sequence) or the sum (for a series). If it diverges
to infinity, state your answer as inf . If it diverges to negative
infinity, state your answer as -inf . If it diverges without being 7. (1 point)
infinity or negative infinity, state your answer as div . Consider the series:
∞
5n ∞
(a) The series ∑ 4n + 11 . 3 3
∑ −
n=1 k=4 (k − 1)2 k2
5n
(b) The sequence .
4n + 11 a) Determine whether the series is convergent or divergent:
Correct Answers: .
• inf (Enter ”conv ” or ”div ” as appropriate.)
• 1.25 b) If it converges, find its sum: .
4. (1 point) Find the values of p for which the series con- If the series diverges, enter here div again.
Correct Answers:
verges.
∞
ln n • CONV
∑ n2p • 0.333333333333333
n=1
Answer (in interval notation):
1
Assignment Homework 9 due 9/12/14 at 9pm
Note: if you need help with formatting your entry in interval
1. (1 point) notation please click here.
Given: Correct Answers:
40
An = n • (0.5,infinity)
4
Determine:
(a) whether {An }is convergent.
If convergent, enter the limit of convergence. If not, enter div . 5. (1 point) Determine whether the series is convergent or
divergent. If convergent, find the sum; if divergent, enter div .
∞
(b) whether ∑ An is convergent.
∞
n=1 3
Correct Answers: ∑ sin(6n) −
n=1 n
• 0
• 13.3333333333333
Answer:
2. (1 point) Correct Answers:
Given: • div
1
An = 0.96
n
Determine:
6. (1 point)
(a) whether {An }is convergent.
If the following series converges, compute its sum. If it di-
If convergent, enter the limit of convergence. If not, enter div .
verges to infinity, state your answer as inf . If it diverges to
∞ negative infinity, state your answer as -inf . If it diverges with-
(b) whether ∑ An is convergent. out being infinity or negative infinity, state your answer as div .
n=1
Correct Answers:
∞
• 0
• div ∑ (e−3n − e−3(n+1) )
n=1
3. (1 point) Let
5n
an = .
4n + 11
For the following answer blanks, decide whether the given se- Correct Answers:
quence or series is convergent or divergent. If convergent, enter • 0.0497870683678639
the limit (for a sequence) or the sum (for a series). If it diverges
to infinity, state your answer as inf . If it diverges to negative
infinity, state your answer as -inf . If it diverges without being 7. (1 point)
infinity or negative infinity, state your answer as div . Consider the series:
∞
5n ∞
(a) The series ∑ 4n + 11 . 3 3
∑ −
n=1 k=4 (k − 1)2 k2
5n
(b) The sequence .
4n + 11 a) Determine whether the series is convergent or divergent:
Correct Answers: .
• inf (Enter ”conv ” or ”div ” as appropriate.)
• 1.25 b) If it converges, find its sum: .
4. (1 point) Find the values of p for which the series con- If the series diverges, enter here div again.
Correct Answers:
verges.
∞
ln n • CONV
∑ n2p • 0.333333333333333
n=1
Answer (in interval notation):
1
