A sequence{an} is given by a1=sqrt (2), an+1=sqrt (2+an).

a) by induction or otherwise, show that {an} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim n-->infinity an exists.

b) Find lim n-->infinity an.

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A sequence{an} is given by a1=sqrt (2), an+1=sqrt (2+an).a) by induction or otherwise, show that {an} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim n-->infinity an exists.b) Find lim n-->infinity an.

A sequence{an} is given by a1=sqrt (2), an+1=sqrt (2+an).

a) by induction or otherwise, show that {an} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim n-->infinity an exists.

b) Find lim n-->infinity an.