Mark all the true statements about sequences of real numbers. Every sequence has a convergent subsequence. Every sequence has a monotonic subsequence. Every subsequence of a divergent sequence diverges. Every subsequence of a convergent sequence converges. Every sequence has a bounded subsequence.

Q: 4 Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence…

A: A sequence is said to be decreasing and bounded if an>an+1.

Q: Decide whether or not the infinite sequence is a cauchy sequence. If it is not a cauchy sequence,…

A:

Q: Give an example, including explanation, which shows that the following statement is false. “If a…

A: Given If a sequence is convergent then it is bounded and monotone. We have to give a example which…

Q: Every bounded sequence converges. True or False?

A: False

Q: Call a three-term strictly increasing arithmetic sequence of integers special if the sum of the…

A: Assume the first terms and the common difference. Let first term be a-d and common difference be…

Q: In 3n an = In 5n

A:

Q: The sequence (c} diverges.

A: To check whether the sequence diverges