PP 12.5_1 - Alternating Series These are series whose terms...

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Unformatted text preview: Alternating Series These are series whose terms are alternately positive and negative. n n n a =- 1 ) 1 ( n n n a =-- 1 1 ) 1 ( n n n a = +- 1 1 ) 1 ( Comments The p-series test and the Comparison Tests only apply to series with positive terms. The Geometric Series Test can be used for series with positive terms as well as for alternating series since | r | controls the behavior of the series. The Test for Divergence applies to all types or series, but has limited use. Example e. convergenc for 3 2 ) 1 ( Test 1 n n n = - This is clearly an alternating series since the powers of 1 become 1 or 1 as n runs over the integers. 1 1 1 1 3 2 3 2 3 2 3 2 ) 1 (- = = = - - = - = - n n n n n n n So, we have a geometric series with | r = -2/3| < 1 ....
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This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.

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PP 12.5_1 - Alternating Series These are series whose terms...

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