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
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
question b
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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