Types of series and tests for convergences

Chapter 9 Infinite Series

MATH- 102Calculus-II

Calculus, 8/E by Howard Anton, Irl Bivens, and Stephen DavisCopyright © 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

2ncan be written

is the Greek capital letter S, used for Sum

1st value of n

last value of n


9.3 INFINITE SERIES (pg:614)


Definition 9.3.1 (p. 614) INFINITE SERIES


Definition 9.3.2 (p. 616)



Theorem 9.3.3 (p. 617)


Figure 9.3.4 (p. 620)


9.4 Convergence Tests (pg: 623)


Theorem 9.4.1 (p. 624)The Divergence Test


Theorem 9.4.2 (p. 624)


Theorem 9.4.3 (p. 625)


Theorem 9.4.4 (p. 626)The Integral Test


Figure 9.4.1 (p. 626)


Theorem 9.4.5 (p. 629)Convergence of p-Series


9.5 The Comparison, Ratio, and Root Tests (pg: 629)


Theorem 9.5.1 (p. 631)The Comparison Test


Figure 9.5.1 (p. 632)


Theorem 9.5.4 (p. 633)The Limit Comparison Test


Theorem 9.5.5 (p. 634)The Ratio Test


Theorem 9.5.6 (p. 635)The Root Test


Equations (1) and (2) (p. 638)

Alternating Series


9.6 Alternating Series (pg: 638)




Theorem 9.6.4 (p. 642)


Theorem 9.6.5 (p. 644)Ratio Test for Absolute Convergence



Page 645Summary of Convergence Tests


Page 645 Summary of Convergence Tests





Figure 9.7.3 (p. 654)

Types of series and tests for convergences

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