5. Let s > 0 and t> 0, and let (ao. a1, a2,, an...) be sequence that satisfies and ao 2-t/s a+1 (18)a, +t (*) for each i0. We will prove an inequality that is important for deriving the global error in Euler's method. (a) Show that (*) implies 1 +1 (1+8)a-1+ [1 + (1+8)] (b) Show that (*) and part (a) imply 0+1(1+s) 2+1+(1+s)+(1+8)] (c) Use an inductive argument to show that a+1(1+s)+1ao+t[1+ (1+s) + (1+s)+...+(1+s)'] (d) The term in brackets [1+ (1+s)+...+(1+s)] is a geometric series. Use this fact to rewrite the inequality from (c) as +1 (1+8)+1(+) S (e) Finally use your answer from 04 to conclude