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SUMMARY OF TESTS. 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.
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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
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
121 141 PART-1: Series with positive terms • 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 122 151 Divg Test Integral Tst Compar Tst LimComp Ratio Tst Root Tst AltSer Tst
151 121 PART-1: Series with positive terms • 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 141 122 Divg Test Integral Tst Compar Tst LimComp Ratio Tst Root Tst AltSer Tst
Types of questions in the exam 1) Determine whether convg or divg AC,CC 2) Find the sum s 3-types 5) Partial sums and their properties
Extra Problems