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High School Math Calculus Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020

To find whether the given series converges or diverges.

To find whether the given series converges or diverges.

Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020

Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020

6th Edition

ISBN: 9781418300203

Author: Prentice Hall

Publisher: Prentice Hall

See similar textbooks

Question

Chapter 9.5, Problem 1QQ

a.

To determine

To find: To find whether the given series converges or diverges.

a.

Expert Solution

Answer to Problem 1QQ

The series converges.

Explanation of Solution

Given:

The given series $∑n=N∞2n2+1$ .

Formula used:

$a=f(n)$ where $f$ is a continuous, positive, decreasing function of x for all $x≥N$ (N is a positive integer).

Then the series $∑n=N∞an$ and the integral $∫N∞f(x)dx$ either both converges or both diverges.

Calculation:

Given series is $∑n=N∞2n2+1$

Using Limit comparing test,

$limx→∞2n2+11n2=limx→∞2x2n2+1limx→∞2n2+11n2=2$

The integral test applies because $∫N∞1xdx$

By p-series test, $∫N∞1xpdx$ converges if $p>1$ , and diverges if $p≤1$ .

It is of the form of $∫N∞1xpdx$ where $p=43$ .

This series converges since $p>1$ .

The limit is positive, $∑n=N∞2n2+1$ also converges.

b.

To determine

To find: To find whether the given series converges or diverges.

b.

Expert Solution

Answer to Problem 1QQ

The series converges.

Explanation of Solution

Given:

The given series $∑n=N∞2n−13n+1$ .

Formula used:

$a=f(n)$ where $f$ is a continuous, positive, decreasing function of x for all $x≥N$ (N is a positive integer).

Then the series $∑n=N∞an$ and the integral $∫N∞f(x)dx$ either both converges or both diverges.

Calculation:

Given series is $∑n=N∞2n−13n+1$ .

Using Limit comparing test,

$limx→∞2n−13n+12n3n=limx→∞2n−12n3n+13nlimx→∞2n−13n+12n3n=1$

If the sequence of partial sum has a limit as $n→∞$ , series convergence otherwise the sequence is divergence.

$S=∑n=N∞2n3n$

This is a geometric series whose initial term is zero and common ratio is $12$ .

$S=∑n=N∞2n3n=231−23S=2$

The limit is positive, $∑n=N∞2n2+1$ also converges.

c.

To determine

To find whether the given series converges or diverges.

c.

Expert Solution

Answer to Problem 1QQ

The series converges.

Explanation of Solution

Given:

The given series $∑n=N∞n4n$ .

Formula used:

$a=f(n)$ where $f$ is a continuous, positive, decreasing function of x for all $x≥N$ (N is a positive integer).

Then the series $∑n=N∞an$ and the integral $∫N∞f(x)dx$ either both converges or both diverges.

Calculation:

Given series is $∑n=N∞n4n$ .

$∑n=N∞n4n$

By p-series test, $∫N∞1xpdx$ converges if $p>1$ , and diverges if $p≤1$ .

It is of the form of $∫N∞1xpdx$ where $p=34$ .

This series converges since $p=1$ .

The limit is positive, $∫N∞n4ndx$ also divergence.

Chapter 9.5, Problem 74E

Chapter 9.5, Problem 2QQ

Chapter 9 Solutions

Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020

Ch. 9.1 - Prob. 1QR Ch. 9.1 - Prob. 2QR Ch. 9.1 - Prob. 3QR Ch. 9.1 - Prob. 4QR Ch. 9.1 - Prob. 5QR Ch. 9.1 - Prob. 6QR Ch. 9.1 - Prob. 7QR Ch. 9.1 - Prob. 8QR Ch. 9.1 - Prob. 9QR Ch. 9.1 - Prob. 10QR

Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - Prob. 48E Ch. 9.1 - Prob. 49E Ch. 9.1 - Prob. 50E Ch. 9.1 - Prob. 51E Ch. 9.1 - Prob. 52E Ch. 9.1 - Prob. 53E Ch. 9.1 - Prob. 54E Ch. 9.1 - Prob. 55E Ch. 9.1 - Prob. 56E Ch. 9.1 - Prob. 57E Ch. 9.1 - Prob. 58E Ch. 9.1 - Prob. 59E Ch. 9.1 - Prob. 60E Ch. 9.1 - Prob. 61E Ch. 9.1 - Prob. 62E Ch. 9.1 - Prob. 63E Ch. 9.1 - Prob. 64E Ch. 9.1 - Prob. 65E Ch. 9.1 - Prob. 66E Ch. 9.1 - Prob. 67E Ch. 9.1 - Prob. 68E Ch. 9.1 - Prob. 69E Ch. 9.1 - Prob. 70E Ch. 9.1 - Prob. 71E Ch. 9.1 - Prob. 72E Ch. 9.1 - Prob. 73E Ch. 9.1 - Prob. 74E Ch. 9.1 - Prob. 75E Ch. 9.1 - Prob. 76E Ch. 9.2 - Prob. 1QR Ch. 9.2 - Prob. 2QR Ch. 9.2 - Prob. 3QR Ch. 9.2 - Prob. 4QR Ch. 9.2 - Prob. 5QR Ch. 9.2 - Prob. 6QR Ch. 9.2 - Prob. 7QR Ch. 9.2 - Prob. 8QR Ch. 9.2 - Prob. 9QR Ch. 9.2 - Prob. 10QR Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.2 - Prob. 43E Ch. 9.2 - Prob. 44E Ch. 9.2 - Prob. 45E Ch. 9.2 - Prob. 46E Ch. 9.3 - Prob. 1QR Ch. 9.3 - Prob. 2QR Ch. 9.3 - Prob. 3QR Ch. 9.3 - Prob. 4QR Ch. 9.3 - Prob. 5QR Ch. 9.3 - Prob. 6QR Ch. 9.3 - Prob. 7QR Ch. 9.3 - Prob. 8QR Ch. 9.3 - Prob. 9QR Ch. 9.3 - Prob. 10QR Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - Prob. 17E Ch. 9.3 - Prob. 18E Ch. 9.3 - Prob. 19E Ch. 9.3 - Prob. 20E Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Prob. 23E Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - Prob. 27E Ch. 9.3 - Prob. 28E Ch. 9.3 - Prob. 29E Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - Prob. 32E Ch. 9.3 - Prob. 33E Ch. 9.3 - Prob. 34E Ch. 9.3 - Prob. 35E Ch. 9.3 - Prob. 36E Ch. 9.3 - Prob. 37E Ch. 9.3 - Prob. 38E Ch. 9.3 - Prob. 39E Ch. 9.3 - Prob. 40E Ch. 9.3 - Prob. 41E Ch. 9.3 - Prob. 42E Ch. 9.3 - Prob. 43E Ch. 9.3 - Prob. 44E Ch. 9.3 - Prob. 45E Ch. 9.3 - Prob. 46E Ch. 9.3 - Prob. 47E Ch. 9.3 - Prob. 48E Ch. 9.3 - Prob. 49E Ch. 9.3 - Prob. 50E Ch. 9.3 - Prob. 1QQ Ch. 9.3 - Prob. 2QQ Ch. 9.3 - Prob. 3QQ Ch. 9.3 - Prob. 4QQ Ch. 9.4 - Prob. 1QR Ch. 9.4 - Prob. 2QR Ch. 9.4 - Prob. 3QR Ch. 9.4 - Prob. 4QR Ch. 9.4 - Prob. 5QR Ch. 9.4 - Prob. 6QR Ch. 9.4 - Prob. 7QR Ch. 9.4 - Prob. 8QR Ch. 9.4 - Prob. 9QR Ch. 9.4 - Prob. 10QR Ch. 9.4 - Prob. 1E Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Prob. 10E Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9.4 - Prob. 17E Ch. 9.4 - Prob. 18E Ch. 9.4 - Prob. 19E Ch. 9.4 - Prob. 20E Ch. 9.4 - Prob. 21E Ch. 9.4 - Prob. 22E Ch. 9.4 - Prob. 23E Ch. 9.4 - Prob. 24E Ch. 9.4 - Prob. 25E Ch. 9.4 - Prob. 26E Ch. 9.4 - Prob. 27E Ch. 9.4 - Prob. 28E Ch. 9.4 - Prob. 29E Ch. 9.4 - Prob. 30E Ch. 9.4 - Prob. 31E Ch. 9.4 - Prob. 32E Ch. 9.4 - Prob. 33E Ch. 9.4 - Prob. 34E Ch. 9.4 - Prob. 35E Ch. 9.4 - Prob. 36E Ch. 9.4 - Prob. 37E Ch. 9.4 - Prob. 38E Ch. 9.4 - Prob. 39E Ch. 9.4 - Prob. 40E Ch. 9.4 - Prob. 41E Ch. 9.4 - Prob. 42E Ch. 9.4 - Prob. 43E Ch. 9.4 - Prob. 44E Ch. 9.4 - Prob. 45E Ch. 9.4 - Prob. 46E Ch. 9.4 - Prob. 47E Ch. 9.4 - Prob. 48E Ch. 9.4 - Prob. 49E Ch. 9.4 - Prob. 50E Ch. 9.4 - Prob. 51E Ch. 9.4 - Prob. 52E Ch. 9.4 - Prob. 53E Ch. 9.4 - Prob. 54E Ch. 9.4 - Prob. 55E Ch. 9.4 - Prob. 56E Ch. 9.4 - Prob. 57E Ch. 9.4 - Prob. 58E Ch. 9.4 - Prob. 59E Ch. 9.4 - Prob. 60E Ch. 9.4 - Prob. 61E Ch. 9.4 - Prob. 62E Ch. 9.4 - Prob. 63E Ch. 9.4 - Prob. 64E Ch. 9.5 - Prob. 1QR Ch. 9.5 - Prob. 2QR Ch. 9.5 - Prob. 3QR Ch. 9.5 - Prob. 4QR Ch. 9.5 - Prob. 5QR Ch. 9.5 - Prob. 6QR Ch. 9.5 - Prob. 7QR Ch. 9.5 - Prob. 8QR Ch. 9.5 - Prob. 9QR Ch. 9.5 - Prob. 10QR Ch. 9.5 - Prob. 1E Ch. 9.5 - Prob. 2E Ch. 9.5 - Prob. 3E Ch. 9.5 - Prob. 4E Ch. 9.5 - Prob. 5E Ch. 9.5 - Prob. 6E Ch. 9.5 - Prob. 7E Ch. 9.5 - Prob. 8E Ch. 9.5 - Prob. 9E Ch. 9.5 - Prob. 10E Ch. 9.5 - Prob. 11E Ch. 9.5 - Prob. 12E Ch. 9.5 - Prob. 13E Ch. 9.5 - Prob. 14E Ch. 9.5 - Prob. 15E Ch. 9.5 - Prob. 16E Ch. 9.5 - Prob. 17E Ch. 9.5 - Prob. 18E Ch. 9.5 - Prob. 19E Ch. 9.5 - Prob. 20E Ch. 9.5 - Prob. 21E Ch. 9.5 - Prob. 22E Ch. 9.5 - Prob. 23E Ch. 9.5 - Prob. 24E Ch. 9.5 - Prob. 25E Ch. 9.5 - Prob. 26E Ch. 9.5 - Prob. 27E Ch. 9.5 - Prob. 28E Ch. 9.5 - Prob. 29E Ch. 9.5 - Prob. 30E Ch. 9.5 - Prob. 31E Ch. 9.5 - Prob. 32E Ch. 9.5 - Prob. 33E Ch. 9.5 - Prob. 34E Ch. 9.5 - Prob. 35E Ch. 9.5 - Prob. 36E Ch. 9.5 - Prob. 37E Ch. 9.5 - Prob. 38E Ch. 9.5 - Prob. 39E Ch. 9.5 - Prob. 40E Ch. 9.5 - Prob. 41E Ch. 9.5 - Prob. 42E Ch. 9.5 - Prob. 43E Ch. 9.5 - Prob. 44E Ch. 9.5 - Prob. 45E Ch. 9.5 - Prob. 46E Ch. 9.5 - Prob. 47E Ch. 9.5 - Prob. 48E Ch. 9.5 - Prob. 49E Ch. 9.5 - Prob. 50E Ch. 9.5 - Prob. 51E Ch. 9.5 - Prob. 52E Ch. 9.5 - Prob. 53E Ch. 9.5 - Prob. 54E Ch. 9.5 - Prob. 55E Ch. 9.5 - Prob. 56E Ch. 9.5 - Prob. 57E Ch. 9.5 - Prob. 58E Ch. 9.5 - Prob. 59E Ch. 9.5 - Prob. 60E Ch. 9.5 - Prob. 61E Ch. 9.5 - Prob. 62E Ch. 9.5 - Prob. 63E Ch. 9.5 - Prob. 64E Ch. 9.5 - Prob. 65E Ch. 9.5 - Prob. 66E Ch. 9.5 - Prob. 67E Ch. 9.5 - Prob. 68E Ch. 9.5 - Prob. 69E Ch. 9.5 - Prob. 70E Ch. 9.5 - Prob. 71E Ch. 9.5 - Prob. 72E Ch. 9.5 - Prob. 73E Ch. 9.5 - Prob. 74E Ch. 9.5 - Prob. 1QQ Ch. 9.5 - Prob. 2QQ Ch. 9.5 - Prob. 3QQ Ch. 9.5 - Prob. 4QQ Ch. 9 - Prob. 1RWDT Ch. 9 - Prob. 2RWDT Ch. 9 - Prob. 3RWDT Ch. 9 - Prob. 4RWDT Ch. 9 - Prob. 5RWDT Ch. 9 - Prob. 6RWDT Ch. 9 - Prob. 7RWDT Ch. 9 - Prob. 8RWDT Ch. 9 - Prob. 9RWDT Ch. 9 - Prob. 10RWDT Ch. 9 - Prob. 1RE Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Prob. 28RE Ch. 9 - Prob. 29RE Ch. 9 - Prob. 30RE Ch. 9 - Prob. 31RE Ch. 9 - Prob. 32RE Ch. 9 - Prob. 33RE Ch. 9 - Prob. 34RE Ch. 9 - Prob. 35RE Ch. 9 - Prob. 36RE Ch. 9 - Prob. 37RE Ch. 9 - Prob. 38RE Ch. 9 - Prob. 39RE Ch. 9 - Prob. 40RE Ch. 9 - Prob. 41RE Ch. 9 - Prob. 42RE Ch. 9 - Prob. 43RE Ch. 9 - Prob. 44RE Ch. 9 - Prob. 45RE Ch. 9 - Prob. 46RE Ch. 9 - Prob. 47RE Ch. 9 - Prob. 48RE Ch. 9 - Prob. 49RE Ch. 9 - Prob. 50RE Ch. 9 - Prob. 51RE Ch. 9 - Prob. 52RE Ch. 9 - Prob. 53RE Ch. 9 - Prob. 54RE Ch. 9 - Prob. 55RE Ch. 9 - Prob. 56RE Ch. 9 - Prob. 57RE Ch. 9 - Prob. 58RE Ch. 9 - Prob. 59RE Ch. 9 - Prob. 60RE Ch. 9 - Prob. 61RE Ch. 9 - Prob. 62RE Ch. 9 - Prob. 63RE Ch. 9 - Prob. 64RE Ch. 9 - Prob. 65RE Ch. 9 - Prob. 66RE Ch. 9 - Prob. 67RE Ch. 9 - Prob. 68RE Ch. 9 - Prob. 69RE Ch. 9 - Prob. 70RE Ch. 9 - Prob. 71EP Ch. 9 - Prob. 72EP Ch. 9 - Prob. 73EP

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