Chapter 10 sequences Series Tests find radius of convg R geometric + telescoping Mac series + important 7 Taylor Binomial

SUMMARY OF TESTS Special Series: Series Tests Geometric Series Harmonic Series Telescoping Series Alter Harmonic p-series Alternating p-series Divergence Test Integral Test Comparison Test Limit Compar Test Ratio Test Root Test Alter Series Test

STRATEGY FOR TESTING SERIES PART-1: Series with positive terms STRATEGY FOR TESTING SERIES Divg Test factorial: ratio test  comp+lim comp power of n: root test easy to integrate: integral test similar to geometric: try comp+lim comp Similar to p-series: try comp+lim comp PART-2: Alternating Series Study (use PART-1) convg divg use alt.-Test AC convg divg CC PART-3: Series with some negative terms REMARK: For multiple-choice-question: before you start read the alternatives first. It guides you to which tests you need to use. Study (use PART-1) convg divg AC

POWER SERIES 1 2 3 1 2 How to find R = radius of convergence Find: (L is a function of x only) Use ratio test: 3 How to find interval of convergence Find R: 1 Study convg at endpoints: a+R and a-R 2

Important Maclaurin Series and Their Radii of Convergence MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620 Denominator is n! even, odd Denominator is n odd

TAYLOR SERIES Maclaurin series ( center is 0 ) Taylor series ( center is a )

THE RATIO AND ROOT TESTS TERM-082

ABSOLUTE CONVERGENCE AND THE RATIO AND ROOT TESTS TERM-082

ABSOLUTE CONVERGENCE AND THE RATIO AND ROOT TESTS TERM-082

POWER SERIES Final-101

POWER SERIES Final-082

POWER SERIES Final-102

POWER SERIES Final-092

POWER SERIES Final-092

POWER SERIES Final-102