Question: Consider the sequence given by f1 = 2 = 1 and fn+2 = fn+1 + fn. Let an = = fn+1/fn. 1 1+an-2 1+

Consider the sequence given by f1 = 2 = 1 and fn+2 = fn+1 + fn. Let an = = fn+1/fn. 1 1+an-2 1+ 1 an-1 (b) Show an an-2 has the same sign as an-2 (c) Show that a2n is a decreasing sequence bounded below by 1. (d) Show that a2n+1 is an increasing sequence bounded above by 2. (e) Show that an converges and find its limit. (a) Show that an = = 2 - an-4.

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