Unformatted text preview: If the limit equals one, you cannot conclude anything. You must try a different test. You know this series converges absolutely because it is a geometric series with a base that is positive and less than one. Will the ratio test agree that the series converges? To apply the ratio test, you need to take the limit of the ratio of two consecutive terms a n +1 and a n . Don’t forget the absolute value symbol! Since you have a fraction over a fraction, invert and multiply. The terms are already positive, so you can remove the absolute value symbol. Canceling 5 n leaves one in the numerator and five in the denominator. Use the Greek letter rho ( ρ ) to represent the value of the limit. Since ρ is less than one, the series converges absolutely. Remember, if ρ equals one, you cannot conclude anything. Use another test. The series might converge like this p-series does, or it might diverge....
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- Spring '10
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