1. (a) Let an = n'/n-1. Note that, for each n EN, a, is non-negative and n = (an+1)". Use the Binomial Formula to prove that, for every n E N, п(п - 1) n 2 and thus a, < 2 for n > 1. (b) Use part (a) (and any other previously proved results) to prove that lim n'/n = 1.

1. (a) Let an = n'/n-1. Note that, for each n EN, a, is non-negative and n = (an+1)". Use the Binomial Formula to prove that, for every n E N, п(п - 1) n 2 and thus a, < 2 for n > 1. (b) Use part (a) (and any other previously proved results) to prove that lim n'/n = 1.

Name: 1. (a) Let an =n'/n-1. Note that, for each n E N, an is non-negative
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Description: 1. (a) Let an =n'/n-1. Note that, for each n E N, an is non-negative and n = (an+1)".Use the Binomial Formula to prove that, for every n E N,п(п - 1)n2and thus a, 1.(b) Use part (a) (and any other previously proved results) to prove that l

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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