1 does the sequence n n 2 does the sequence worksheet 3n 4 converge if

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Question

1. Does the sequence
{
n-
n²
2. Does the sequence
Worksheet
3n² +4
converge? If so, what is the limit? If not, why not?
(In(13)) converge? If so, what is the limit? If not, why not?
n+2
3. Does the sequence
{
n
n²
2
n
converge? If so, what is the limit? If not, why not?
4. Does the sequence {n sin(1/n)} converge? If so, what is the limit? If not, why not? 5. Does the sequence {n} converge? If so, what is the limit? If not, why not?
6. Does the sequence {n} converge? If so, what is the limit? If not, why not?
7. Find lim
n→x
n
2n 8. Find lim 31/n
n→X
9. Find lim ™”, where r is some real number. Does your answer depend on what r is? If
n→x
so, explain how. If not, explain why. (This may be a good question to discuss on the
discussion board.) 10. Is the sequence {n²} bounded? Is it monotone?
11. Suppose {an} is a sequence of positive numbers and an > n². Must {an} converge? Why
or why not?
12. Suppose {an} is a sequence of positive numbers and an < 12. Must {an} converge? Why
or why not?
13. Are the following always true or may be false? Explain completely.
(a) {sin(n)} is both increasing and decreasing.
(b) Every sequence that is both increasing and decreasing must converge.
(c) Strictly increasing sequences must diverge.