sn8_1 - Math 1432 Notes session 8 11.1 Infinite Series The...

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Unformatted text preview: Math 1432 Notes session 8 11.1 Infinite Series The infinite series: = k k a What this means = k k a = If terms 0, then An infinite series will converge IF the sequence (list) of PARTIAL SUMS converges. Ex: 1 2 k k = If the sequence of partial sums {s n } converges to a finite limit L we write L a k k = = and say that = k k a converges to L and L is the sum of the series. Geometric Series: ,... , , , 1 3 2 x x x is a geometric series. We write: = k k x If 1 < x then x x k k- = = 1 1 If 1 x then = k k x diverges Note: ( 29 r r r N N n n-- = + = 1 1 1 for any r Ex: 1. 5 3 k k = 2. 7 9 k k = 3. 3 4 k k = - 4. ( 29 2 k k =- General Properties: If = k k a converges and = k k b converges, then ( 29 = + k k k b a converges If = k k a converges, then = k k a converges ( = k k a = ) Thm If = k k a converges then k a as k ....
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This note was uploaded on 03/07/2012 for the course MATH 11278 taught by Professor Jeffmorgan during the Summer '10 term at University of Houston.

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sn8_1 - Math 1432 Notes session 8 11.1 Infinite Series The...

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