## Exam Information

Login / Sign Up to View Document

## Sample Document Text

Series Handout
Tests for Convergence or Divergence
Test Name IF THEN
Geometric Series jrj< 1 (jrj 1) P1n=0crn converges (diverges)
also, sn = c1 rn1 r and sn! c1 r
Tests for series with positive terms
Integral Test R1N f(x) dx converges P1n=0f(n) converges
p-Series p> 1 (p 1) P1n=1 1=np converges (diverges)
Comparison Test an bn and Pbn converges Pan converges
an bn and Pbn diverges Pan diverges
Ratio Test an+1an ! and < 1 ( > 1) Pan converges (diverges)
Tests for series with terms of any sign
Limit Test (nth term test) limn!1an6= 0 Pan diverges
Alternating Series Test P( 1)nun with 1) un 0 P( 1)nun converges
2) un un+1 and 3) un!0
Absolute Convergence Test Pjanjconverges Pan converges
Behavior of Power Series
Corollary to Theorem 18 The convergence of the series Pcn(x a)n is described by one of the following
three possibilities:
1. There is a positive number R such that the series diverges for x withjx aj>R but converges absolutely
for x with jx aj< R. The series may or may not converge ...

© Copyright 2019 , Koofers, Inc. All rights reserved.

The information provided on this site is protected by U.S. and International copyright law, and other applicable intellectual property laws, including laws covering data access and data compilations. This information is provided exclusively for the personal and academic use of students, instructors and other university personnel. Use of this information for any commercial purpose, or by any commercial entity, is expressly prohibited. This information may not, under any circumstances, be copied, modified, reused, or incorporated into any derivative works or compilations, without the prior written approval of Koofers, Inc.