Answered: the following saries is absolutely…

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Calculus

the following saries is absolutely Conditionaly convesge check iR Conv. or divergent (1-) 3 ca!)? (en) ! nニ

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

100%

the following saries is absolutely
Conditionaly convesge
check iR
Conv.
or divergent
(1-) 3
ca!)?
(en) !
nニ

Expert Solution

Step 1

We use following test to check the convergence:

Ratio Test: Suppose we have the series:

Define,

a) If L < 1, given series is absolutely convergent (hence convergent)

b) If L > 1, given series is divergent

c) If L = 1, test is inconclusive

Step 2

Series given in the question:

Consider

Divide top and bottom by n

Here L = 1/4 < 1 and hence the given series is absolutely convergent by Ratio Test

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