Question: really need some help . Consider the sequence (a) satisfying the recurrence an - 2an-1 + 40.-2 -80-3- Let On = Ox - 20.-1- (a)

really need some help

. Consider the sequence (a) satisfying the recurrence an - 2an-1 + 40.-2 -80-3- Let On = Ox - 20.-1- (a) Show that b., - 450-2 = 0. (1) and that by = A . 2" + B (-2)" 2 is the general solution for the sequence (b)- [5) (b) Prove, by Induction on k, that an = KA . 2" + B . (-2)"-1 ((-1)' - 1) +2tan-*, for k 2 1. Deduce that On - nA . 2" - B . 20-1 - B . (-2)"-1+2"20- [8]

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