TestsForSeries

TestsForSeries - A. Alaca MATH 1005A MATH 1005 A WINTER...

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A. Alaca MATH 1005A Winter 2007 1 MATH 1005 A WINTER 2007 LECTURE SLIDES Prepared by Ay¸ se Alaca Last modifed: February 5, 2007
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A. Alaca MATH 1005A Winter 2007 2 INFINITE SEQUENCES AND SERIES Defnition: Let ± n =1 a n be an infnite series and let s n = n ± i =1 a i . IF the sequence ( s n ) is convergent and lim n -→∞ s n = s , then we say that ± n =1 a n is convergent, and we call s the sum oF the series, and we write ± n =1 a n = s. lim n -→∞ s n = s ⇐⇒ ± n =1 a n = s. IF ( s n ) is divergent, then ± n =1 a n is also divergent. Defnition: The series given by ± n =1 ar n - 1 = a + ar + ar 2 + ··· + ar n - 1 + ··· ,a ± =0 . is called the geometric series with ratio r . ± n =1 ar n - 1 = lim n -→∞ s n = lim n -→∞ a (1 - r n ) 1 - r = a 1 - r , iF - 1 <r< 1 divergent , iF r> 1or r ≤- 1 . = a 1 - r , iF | r | < 1 divergent , iF | r |≥ 1 .
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This note was uploaded on 01/19/2010 for the course MATH 1005 taught by Professor Any during the Fall '07 term at Carleton CA.

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TestsForSeries - A. Alaca MATH 1005A MATH 1005 A WINTER...

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