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9 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Geometric Series
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Summation 0 to infinity of a*r^k
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Converges to a/(1-r) if abs(r)<1 |
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kth Term Test
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All series
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if limit of asubk as k approaches infinity doesn't equal zero, it diverges |
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Integral Test
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Summation from 1 to inf. of asubk where asubk is some continuous function of k, decr, and always greater than zero
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the summation and the integral of f(k) on the same interval either both converge or both diverge |
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p-Series Test
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The one with 1/k^p
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Converges for p>1, diverges for p> or = 1 |
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Comparison Test
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you have 2 summations, where one nth term is always greater than the other
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If the greater one converges, the lesser one converges. If the lesser one diverges, the great one diverges. |
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Limit Comparison Test
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2 summations, both nth terms are greater than zero, and the limit of one over the other is greater than zero
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Both Converge or both diverge |
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Absolute Convergence
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Series with some positive and negative terms(including alternating series)
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if abs of summation converges, then the summation converges absolutely |
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Ratio Test
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Any series
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limit as k approaches inf. of abs(asub(k+1)/asubk) If it's less than 1 Converges If it's greater than 1 Diverges |
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Root Test
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Any series
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kth root of abs of asubk |
