chap11sec4

chap11sec4 - 11.4 The Comparison Tests

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11.4 The Comparison Tests The comparison test can be applied to series with  positive terms. Comparison Test Suppose that the series  , n n a b  are both series with positive terms. (i) If  n b is convergent and  n n a b  for all n, then  n a is also convergent. (ii) If  n b is divergent and  n n a b  for all n, then  n a is also divergent. When using the comparison test we can use p-series (including the harmonic series) and geometric series because we can  determine convergence or divergence easily. Don't confuse geometric series,  n ar , with p-series,  1 p n . To show convergence, the terms of the series being tested must be   less than those of the convergent series selected for  comparison. Example:  Determine convergence or divergence for  3 1 1 n n n = + .   
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chap11sec4 - 11.4 The Comparison Tests

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