Question: 4. Define the sequence In as follows: given the initial value x1, find recursively Zn+1 = an+1 for n = 2, 3, .... Show that

4. Define the sequence In as follows: given the initial value x1, find recursively Zn+1 = an+1 for n = 2, 3, .... Show that regardless of the initial value x, the sequence In is not convergent. 5. Let x be a real number. Show that there exists a sequence of rational numbers, an, such that an > x for all n and an > x as n - 0

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