A sequence {an} converges if: O limn→∞ an 0 O limn→∞ an does not exist. limn→∞ ɑn_exists. O None of these.

Q: == 2.9 Let (an) be a sequence with limit a, and define bɲ = an+1 (n = 1, 2,...). Show that (bn) → a.

A: We know that  A sequence an converges to a limit L  if, for any positive real number epsilon there…

Q: Ex: 1. Let (an) and (bn) be two diverge sequence show that whether (an + bn) is converge or diverge…

A: Multiple :    Let , an  ,  bn are two divergent sequence. We need to check that whether an + bn…