Question

If (sn) is an unbounded increasing sequence, then lim sn=

A. 0
B. [infinity] (infinity)
C. -[infinity] (negative infinity)
D. 1

Answer 1

If (sn) is an unbounded increasing sequence, then the limit of sn is [infinity].

Step-by-step explanation:

If (sn) is an unbounded increasing sequence, then the limit of sn is B. [infinity] (infinity).

To see why, let's consider the definition of an unbounded increasing sequence. An unbounded increasing sequence is a sequence in which the terms get larger and larger without limit. In other words, there is no upper bound on the terms of the sequence. As the terms of the sequence get larger and larger, the limit of the sequence approaches infinity.

For example, let's say we have the sequence (1, 2, 3, 4, 5, ...). As we continue the sequence, the terms keep increasing without bound. Therefore, the limit of this sequence is infinity.