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.

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