Let (an)neN be the sequence with a₁ = = 2 and an+1 = √16an 15 for all n = 1, 2, 3, . . .. (a) Show that (an)neN is bounded above. (b) Show by induction that (an)neN is increasing. (c) Explain why (an)neN converges in R. (d) Determine lim an (and justify your answer). n→∞ (e) What is sup{an : n € N}? Justify your answer.

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…