Question: A sequence {an} is given by a1 = 2, an+1= 2 + an. (a) By induction or otherwise, show that {an} is increasing and bounded

A sequence {an} is given by a1 = √2, an+1=√ 2 + an.
(a) By induction or otherwise, show that {an} is increasing and bounded above by 3. Apply Theorem 11 to show that lim n→∞ an exists
(b) Find lim n→∞ an.

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