series test

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

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Strategy for Testing Series 1. If the series is of the form X 1 n p , it is a p -series , which we know to be convergent if p > 1 and divergent if p 1. 2. If the series has the form X ar n - 1 or X ar n , it is a geometric series , which converges if | r | < 1 and diverges if | r | ≥ 1. Some preliminary algebraic manipulation may be required to bring the series into this form. 3. If the series has a form that is similar to a p -series or a geometric series, then one of the comparison tests (Theorems 10, 11) should be considered. In particular, if a n is a rational function or an algebraic function of n (involving roots of polynomials), then the series should be compared with a p -series (The value of p should be chosen by keeping only the highest powers of n in the numerator and denominator). The comparison tests apply only to series with positive terms. If X a n has some negative terms, then we can apply the Comparison Test to X | a n | and test for absolute convergence . 4. If you can see at a glance that lim

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

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