Let (an) be an increasing sequence of real numbers. Select all the true statements below. a. If there exists c ER such that an e for all n then (an) is convergent. □b. If an #0 for all n then is decreasing. c. If there exists c ER such that an ≤ c for all n then every subsequence of (a) is convergent.

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.

Let {n} and {n} be real sequences. Show that if xn → x and yn →y then for all a, ß ER, axn + Byn → ax + By