Types of series and tests for convergences

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The document discusses series and sigma notation in calculus. It explains that a series is the sum of the terms of a sequence. Sigma notation can be used to describe a series, where the Greek letter sigma represents the sum, and the limits of the index variable are specified. The document contains examples and definitions related to series from the textbook "Calculus, 8/E".

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Calculus, 8/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.
Series
When the terms of a sequence are added, we get a series
...,25,16,9,4,1The sequence
gives the series ...2516941 
Sigma Notation for a Series
A series can be described using the general term
100...2516941 e.g.

10
1
2
ncan be written
 is the Greek capital letter S, used for Sum
1st value of n
last value of n

Calculus, 8/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

Calculus, 8/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.
Equations (1) and (2) (p. 638)

Calculus, 8/E by Howard Anton, Irl Bivens, and Stephen Davis
Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.
Definition 9.7.3 (p. 653)

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