If the solution of the recurrence relation αun−1 +βun−2 = f(n),(n ≥ 2) is un = 1−2n+3.2 n , then determine the values of α,β and f(n). (6) b) A bank pays you 4.5% interest per year. In addition, you receive |100 as bonus at the end of the year (after the interest is paid). Find a recurrence for the amount of money after n years if you invest |2000. (4) c) If 5 points are chosen in a square of side 2cm, show that there will always be two points at a distance of at most √ 2cm.
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