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(b) Let {an} be the sequence defined by an = (¹ + ² ) ". (i) Show that {an} is an increasing sequence. (ii) Show that the sequence {an} is bounded above. (iii) Show that the sequence {a} converges to e².

(b) Let {an} be the sequence defined by an = (¹ + ² ) ". (i) Show that {an} is an increasing sequence. (ii) Show that the sequence {an} is bounded above. (iii) Show that the sequence {a} converges to e².

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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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 by dim 1+ 1 n! (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: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 by dim 1+ 1 n! (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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