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1. Let an = 5n 4n3 5 This sequence converges to L = 4 (a) Find the smallest N EN such that |an — L| < 10-4 for all n > N. (b) Show that, for all n > 12, |an - L| < 1/n. Deduce an integer M (not necessarily the smallest!) such that an - L| < 10-6 for all n > M. 1| < 10 101 a 5 (c) Prove from first principles that an converges to .

1. Let an = 5n 4n3 5 This sequence converges to L = 4 (a) Find the smallest N EN such that |an — L| < 10-4 for all n > N. (b) Show that, for all n > 12, |an - L| < 1/n. Deduce an integer M (not necessarily the smallest!) such that an - L| < 10-6 for all n > M. 1| < 10 101 a 5 (c) Prove from first principles that an converges to .

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. Let an = 5n 4n - 3 5 This sequence converges to L = 4 (a) Find the smallest N EN such that an - L| < 10-4 for all n > N. (b) Show that, for all n > 12, |an - L| < 1/n. Deduce an integer M (not necessarily the smallest!) such that an - L| < 10-6 for all n > M. 11 ≤ 10 tot att (c) Prove from first principles that an converges to . 5
Transcribed Image Text:1. Let an = 5n 4n - 3 5 This sequence converges to L = 4 (a) Find the smallest N EN such that an - L| < 10-4 for all n > N. (b) Show that, for all n > 12, |an - L| < 1/n. Deduce an integer M (not necessarily the smallest!) such that an - L| < 10-6 for all n > M. 11 ≤ 10 tot att (c) Prove from first principles that an converges to . 5
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