qiestion a li (1+1)".(a) Define the sequence {b} by b₁ = 2, and for n ≥ 2,Recall that e lim (1+bn = bn-1 +Show that the sequence {bn} converges to e.(b) Let {an} be the sequence defined bydim1+1n!(i) Show that {an} is an increasing sequence.(ii) Show that the sequence {an} is bounded above.(iii) Show that the sequence {an} converges to e².

“Since you have posted multiple questions, we will provide the solution only to the first question…

Answered: lim (1+1)". (a) Define the sequence…

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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lim (1+1)". (a) Define the sequence {bn} by b₁ = 2, and for n ≥ 2, Recall that e lim bn = bn-1 + Show that the sequence {bn} converges to e. 1 n!