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84x n Define the sequence {bn} by b₁ Show that the sequence {bn} con- Let {an} be the sequence defined (i) Show that {an} is an increa

84x n Define the sequence {bn} by b₁ Show that the sequence {bn} con- Let {an} be the sequence defined (i) Show that {an} is an increa

Advanced Engineering Mathematics
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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(¹ + ²) ". (a) Define the sequence {b} by b₁ = 2, and for n ≥ 2, 1 n! Recall that e= lim n4x bn = bn-1 + Show that the sequence {bn} converges to e. (b) Let {an} be the sequence defined by an 2 - (1 + ²)”. = (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.
Transcribed Image Text:(¹ + ²) ". (a) Define the sequence {b} by b₁ = 2, and for n ≥ 2, 1 n! Recall that e= lim n4x bn = bn-1 + Show that the sequence {bn} converges to e. (b) Let {an} be the sequence defined by an 2 - (1 + ²)”. = (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.
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