Question: 1. (20 points) Define the sequence {an} by: 1023, an + 5 an +1' a = an+1 = (a) Show that |an 5| =

1. (20 points) Define the sequence {an} by: 1023, an + 5 an +1' a = an+1 = (a) Show that |an 5| = |an the golden ratio. (b) Hence prove rigorously that n> 1. 5 for all n 2, where = 1.618... is lim an = n 5.

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