hw97 - 9.7 Pages 487-488 # 1-19 odd, 25 1. 1 From the...

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9.7 Pages 487-488 # 1-19 odd, 25 1. From the geometric series for 1 1 x with x replaced by –x, we get 2345 1 1 1 xx x x x x =−+ − + − + + " , radius of convergence 1. 3. 22 3 11 1 2 ; , 1 (1 ) ) ) dd dx x dx x xx  ==   −− 3 1 so ) x is 1 2 of the second derivative of 1 1 x . Thus, 23 3 1 13 6 1 0 ) x x = ++ + + " ; radius of convergence 1. 11. To get the series for 1 ln 1 x x + , we need to notice 1 ln ln(1 ) – ln(1– ) 1– x x x x + =+ . 234 ) , –1 1 xxx x + + < ln(1– ) – – , –1 1 x = +… ≤ < 35 12 2 ln ) ) 2 13 5 x x x + = +− −= + + + radius of convergence 1. 13. Substitute –x for x in the series for x e to get: 1 2! 3! 4! 5! x xxxx ex " . 5. From the geometric series for 1 1 x with x replaced by 3 2 x , we get 1 3 9 2 7 2 1 3 2 2 4 8 1 2 13 9 2 7 24 8 1 6 x x x x + + + + =+ + + + " " ; radius of convergence 2 3 . 32 2 1 1 3 x −< < →−< < → < < 15. Add the result of Problem 13 to the series for x e to get: 246 222 2 6! ee + + + + " .
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This note was uploaded on 02/25/2010 for the course MATH 201 taught by Professor Kim during the Spring '07 term at SIU Carbondale.

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hw97 - 9.7 Pages 487-488 # 1-19 odd, 25 1. 1 From the...

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