Choosing a Convergence Test for Infinite Series Courtesy David J. Manuel Do Series Diverges by the individual No the Divergence Test terms approach 0? Yes Ratio Test Do individual No Does terms have the series factorials or Yes alternate (Ratio of Consecutive exponentials? Yes Terms) signs? No Is individual term Series Test easy to integrate? (Do absolute value of Use Integral Test terms go to 0?) Yes Use Alternating No Comparison Test or Limit Comp. Test Yes (Look at dominating Do individual terms terms) involve fractions with powers of n? No
Choosing a Convergence Test for Infinite Series Courtesy David J. Manuel Do the individual No terms approach 0? Series Diverges by the Divergence Test Yes Does the series alternate signs? No Yes Do individual terms have factorials or exponentials? No Yes Ratio Test (Ratio of Consecutive Terms) Is individual term easy to integrate? No Yes Use Integral Test Use Alternating Series Test (Do absolute value of terms go to 0?) Do individual terms involve fractions with powers of n? No Yes Comparison Test or Limit Comp. Test (Look at dominating terms)
Harolds_Series_Convergence_Tests_Cheat_Sheet_2016.docx