MAT136H1 Study Guide - Midterm Guide: Ratio Test, Conditional Convergence
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MAT136H1 Full Course Notes
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By the word ratio test, it takes and the next term expression and takes a ratio of the two so that: | means is absolutely convergent (ie. convergent) | means no conclusion can be drawn from the ratio test about convergence or divergence of . All series expression falls into one of the three categories, thus depending on the outcome of the ratio test, its convergence, or divergence, or no conclusion can be drawn based on the test. Determine if the series is absolutely convergent conditionally convergent, or divergent. To put into ratio test, is just taking the series expression inside the summation as it is, thus simply replacing. The ratio text requires the next term expression , thus it is then by wherever occurs. Now that these two expressions are written down, the ratio can be taken: | then it can be simplified so that limit value becomes more obvious: |
