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Sequences

Sequences

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.

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 Kan for all n.

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