4. Let {an} be the sequence such that: a1 = 1 and an+1=1+ 1 1+1/an (a)...

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4. Let {an} be the sequence such that: a1 = 1 and an+1=1+ 1 1+1/an (a) Assuming that this sequence converges to a positive number, find the limit L = lim an. n (b) Show that the sequence {an} is bounded above by L. (c) Show that the sequence {an} is increasing for all n 1. (d) Explain why the sequence {an} converges to L. 4. Let {an} be the sequence such that: a1 = 1 and an+1=1+ 1 1+1/an (a) Assuming that this sequence converges to a positive number, find the limit L = lim an. n (b) Show that the sequence {an} is bounded above by L. (c) Show that the sequence {an} is increasing for all n 1. (d) Explain why the sequence {an} converges to L.