MAT136H1 Study Guide - Midterm Guide: Ratio Test, Alternating Series, Conditional Convergence
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Question #3 (medium): alternating series tested using the ratio test. | means is divergent is absolutely convergent (ie. convergent) | means no conclusion can be drawn from the ratio test about convergence or. Notice that the ratio divergence of is inside the absolute value sign. Therefore, even alternating series can be tested for its convergence or divergence using this ratio test. Determine if the series is absolutely convergent, conditionally convergent, or divergent. The given series is an alternating series, however it can still be tested against the ratio test to see any conclusion can be drawn about its convergence, divergence. Since the ratio is placed inside the absolute value sign for the ratio test, the alternating sign component ( ) can be dropped when testing for the ratio test. , then put this ratio into the ratio test: | ( ) | then simplify as much as possible, starting with things like powers:
