series test - Strategy for Testing Series 1 1 If the series is of the form it is a p-series which we know to np be convergent if p > 1 and divergent if

# series test - Strategy for Testing Series 1 1 If the series...

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Strategy for Testing Series1. If the series is of the form1np, it is ap-series, which we know tobe convergent ifp >1 and divergent ifp1.2. If the series has the formarn-1orarn, it is ageometric series,which converges if|r|<1 and diverges if|r| ≥1. Some preliminaryalgebraic manipulation may be required to bring the series into thisform.3. If the series has a form that is similar to ap-series or a geometricseries, then one of thecomparison tests(Theorems 10, 11) shouldbe considered. In particular, ifanis a rational function or an algebraicfunction ofn(involving roots of polynomials), then the series should becompared with ap-series (The value ofpshould be chosen by keepingonly the highest powers ofnin the numerator and denominator). Thecomparison tests apply only to series with positive terms.Ifanhas some negative terms, then we can apply the Comparison Test to|an|and test forabsolute convergence.