(1) A sequence an is given by a₁ = √2, an+1 √2+ an (a) By induction or otherwise, show that a,, is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that exists. (b) Find limn-+0 an.

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A: Answerhamdwritten  an+2 nt1 n+2 on,we pm">