Example 1
Determine if the sequence is increasing, decreasing, or neither.
an = 2n
Example 2
Determine if the sequence is increasing, decreasing, or neither.
Example 3
Determine if the sequence is increasing, decreasing, or neither.
an = (-1)n n2
Example 4
Determine if the sequence is increasing, decreasing, or neither.
an = -n2
Example 5
Determine if the sequence is increasing, decreasing, or neither.
Example 6
Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.
, each term an is between 4 and 5.Example 7
Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.
an = 4 – n
Example 8
Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.
an = (-1)n
Example 9
Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.
an = n3
Example 10
Determine if the sequence is (a) bounded above, (b) bounded below, and (c) bounded or unbounded.
an = (-1)n2n
Example 11
Determine if the statement is true or false. Explain your reasoning.
If a sequence has 5 ≤ an ≤ 6 for all n, then the sequence must converge.
Example 12
Determine if the statement is true or false. Explain your reasoning.
The sequence 1,1,1,1,... is both convergent and bounded.
Example 13
Determine if the statement is true or false. Explain your reasoning.
If a sequence diverges, the sequence is unbounded.
Example 14
Determine if the statement is true or false. Explain your reasoning.
If a sequence is unbounded, that sequence diverges.
Example 15
Determine if the statement is true or false. Explain your reasoning.
If a sequence converges, there is some value K such that K ≤ an for all n.