5 Let 0 and t 0 and let ao 1 a2 n be sequence that satisfies

Last updated: 10/13/2023

5 Let 0 and t 0 and let ao 1 a2 n be sequence that satisfies and a S 1 8 a t for each i20 We will prove an inequality that is important for deriving the global error in Euler s method a Show that implies 1 1 8 a 1 t 1 1 8 b Show that and part a imply 0 1 1 s a 2 t 1 1 s 1 s c Use an inductive argument to show that a 1 1 s 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 t 9 1 1 8 00 e Finally use your answer from 04 to conclude