1. Prove the following statement.If (rn), (sn), (tn) are sequences of real numbers such that8n 2 N; rn  sn  tn and limn!1rn = limn!1tn = s 2 R;thenlimn!1sn = s

{In(8n +1) – In(4n +5)} 20. a. 2 b. 0 c. In(2) d. In(5) e. Divergent

42. Give an example of a sequence of positive rationals {a„}-1 such that the following statement holds: Vr, y so that 0 1 such that x < a, < y.

15. We define a sequence of integers as follows: fo f₁ fn = = 0, 1, fn-1 + fn-2 = for n ≥ 2. The integer fn is called the nth Fibonacci number. Compute the Fi- bonacci numbers fn for n = = 2,3,..., 12. Prove that (fn, fn+1) = 1 for all nonnegative integers n.