4. Let a₁ = √2, andan+1 = √2+ anVn € N.Show that {an} is a monotone sequence by mathematical induction.Show that {an} is bounded by mathematical induction.Show that {an} is a convergent sequence.

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Answered: 4. Let a₁ = √2, and an+1 = √2+ an Vn €…

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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4. Let a₁ = √2, and an+1 = √2+ an Vn € N. Show that {a} is a monotone sequence by mathematical induction. Show that {an} is bounded by mathematical induction. Show that {an} is a convergent sequence.