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Absolute And Conditional Convergence  Definition
9.6 ABSOLUTE AND CONDITIONAL CONVERGENCE Consider a series
which has both positive and negative terms. We may form a new series
whose terms are the absolute values of the terms of the given series. If all the terms a_{n} are nonzero, then a_{n} > 0 so
is a positive term series. If is already a positive term series, then a_{n} = a_{n} and the series is identical to its absolute value series Sometimes it is simpler to study the convergence of the absolute value series than of the given series . This is because we have at our disposal all the convergence tests for positive term series from the preceding sections. DEFINITION A series is said to be absolutely convergent if its absolute value series is convergent. A series which is convergent but not absolutely convergent is called conditionally convergent.


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