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Define {an} by ( a1 = 2, an+1 = 2 + an for n 1. (a) Show that an 2 for all indices n. (b)

Define {an} by ( a1 = 2, an+1 = 2 + an for n 1.

(a) Show that an 2 for all indices n. (b) Show that an+1 > an for all indices n. (c) State how you know that {an} converges. (d)Determine the value of limn an.

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