Explanation Using left endpoints: n = 2 ; 0 + 0.5 = 0.5 n = 4 ; 0 + 0.125 + 0.25 + 0.375 = 0.75 n = 10 ; 0 + 0.02 + 0.04 + 0.06 + … .. + 0.18 = 10 2 ( 0 + 0.18 ) = 0.9 n = 100 ; 0 + 0.0002 + 0.0006 + … … + 0.0198 = 100 2 ( 0 + 0.0198 ) = 0.99 Using right endpoints: n = 2 ; 0...

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 14.5, Problem 31AYU

To determine

To verify: The entries in the below table:

Using Left end points $n$ 2 4 10 100

Area $0 .5$ $0 .75$ $0 .9$ $0 .99$

Using right end points $n$ 2 4 10 100

Area $1 .5$ $1 .25$ $1 .1$ $1 .01$

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Chapter 14.5, Problem 30AYU

Chapter 14.5, Problem 32AYU

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To verify: The entries in the below table: Using Left end points n 2 4 10 100 Area 0 .5 0 .75 0 .9 0 .99 Using right end points n 2 4 10 100 Area 1 .5 1 .25 1 .1 1 .01

Solution Summary: The author explains how to use left and right endpoints in the table.

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To verify: The entries in the below table:

Using Left end points $n$ 2 4 10 100

Area $0 .5$ $0 .75$ $0 .9$ $0 .99$

Using right end points $n$ 2 4 10 100

Area $1 .5$ $1 .25$ $1 .1$ $1 .01$

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Chapter 14 Solutions

Additional Math Textbook Solutions

Using Left end points	$n$	2	4	10	100
Using Left end points	Area	$0 .5$	$0 .75$	$0 .9$	$0 .99$
Using right end points	$n$	2	4	10	100
Using right end points	Area	$1 .5$	$1 .25$	$1 .1$	$1 .01$

To verify: The entries in the below table: Using Left end points n 2 4 10 100 Area 0 .5 0 .75 0 .9 0 .99 Using right end points n 2 4 10 100 Area 1 .5 1 .25 1 .1 1 .01

Solution Summary: The author explains how to use left and right endpoints in the table.

Concept explainers

Videos

To verify: The entries in the below table: Using Left end points n 2 4 10 100 Area 0.5 0.75 0.9 0.99 Using right end points n 2 4 10 100 Area 1.5 1.25 1.1 1.01

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

To verify: The entries in the below table:

Using Left end points $n$ 2 4 10 100

Area $0 .5$ $0 .75$ $0 .9$ $0 .99$

Using right end points $n$ 2 4 10 100

Area $1 .5$ $1 .25$ $1 .1$ $1 .01$