The sequence {un} is given by the recurrence relation Ип+1 Зиn + 37+2 for n 0, 1, 2, 3, ..., and initial value uo = = 0. (a) Showing your working, use the recurrence relation to compute uj, И2, из, и4 аnd us- (b) Prove by induction that Un — п3"+1 for all n > 0.

The sequence {un} is given by the recurrence relation Ип+1 Зиn + 37+2 for n 0, 1, 2, 3, ..., and initial value uo = = 0. (a) Showing your working, use the recurrence relation to compute uj, И2, из, и4 аnd us- (b) Prove by induction that Un — п3"+1 for all n > 0.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The sequence {un} is given by the recurrence relation
Ип+1
3un + 3"+2 for n= 0,1,2,3, . . . ,
and initial value uo = 0.
(a) Showing your working, use the recurrence relation to
compute uj, u2, Из, ид аnd uз.
(b) Prove by induction that
Un = n3"+1 for all n > 0.

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