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ch11s4

# ch11s4 - 11.4 The Comparison Tests The comparison test can...

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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 are both series with positive terms. , n a n b n n (i) If is convergent and for all n, then is also convergent. n b n a b n a (ii) If is divergent and for all n, then is also divergent. n b n a b n a 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, , with p-series, n ar 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 = + . To show divergence, the terms of the series being tested must be greater than those of the divergent series selected for comparison.

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