1. Determine the limits of the following sequences if they converge. If they do not convergeexplain why.a. anthe units digit of n.nb. an =COSn+1c. an is defined by a1 = 1 and an+1 = .123456789a,.

Name: 1. Determine the limits of the following sequences if they converge.
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Description: 1. Determine the limits of the following sequences if they converge. If they do not convergeexplain why.a. anthe units digit of n.nb. an =COSn+1c. an is defined by a1 = 1 and an+1 = .123456789a,.

Answered: 1. Determine the limits of the…

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. Determine the limits of the following sequences if they converge. If they do not converge
explain why.
a. an
the units digit of n.
n
b. an =
COS
n+1
c. an is defined by a1 = 1 and an+1 = .123456789a,.

Expert Solution

Step 1

Part (a)

We shall use d'alembert's ratio test which states that sequence $\{a_{n}\}$ converges if

$\lim_{n \to \infty} |\frac{a_{n + 1}}{a_{n}}| < 1$

Here $a_{n}$ can take values from $0 - 9$ .

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