Natural Science Department Duy Tan University Strategy for

Natural Science Department – Duy Tan University Strategy for Testing Series We will learn about: The. ways of testing a series for convergence or divergence. Lecturer: Ho Xuan Binh Da Nang-09/2013

Natural Science Department – Duy Tan University 1 Strategy 1 If the series is of the form: It is a p-series We know this to be convergent if p > 1 and divergent if p ≤ 1. Strategy for Testing Series

Natural Science Department – Duy Tan University 2 Strategy 2 If the series is of the form: It is a geometric series We know this to be convergent if |r | < 1 and divergent if |r | ≥ 1. Strategy for Testing Series

Natural Science Department – Duy Tan University 3 Strategy 3 If the series has a form that is similar to a p-series or a geometric series One of the comparison tests should be considered Strategy for Testing Series

Natural Science Department – Duy Tan University 4 Strategy 4 If you can see at a glance that : The Test for Divergence should be used Strategy for Testing Series

Natural Science Department – Duy Tan University 5 Strategy 5 If the series is of the form : The Alternating Series Test is an obvious possibility Strategy for Testing Series

Natural Science Department – Duy Tan University 6 Strategy 6 Series that involve factorials or other products (including a constant raised to the nth power) are often conveniently tested using the Ratio Test. Strategy for Testing Series

Natural Science Department – Duy Tan University 7 Strategy 7 If an is of the form : The Root Test may be useful Strategy for Testing Series

Natural Science Department – Duy Tan University 8 Strategy 8 If an=f(n), where is easily evaluated The Integral Test is effective Strategy for Testing Series

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