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Pre-Calc Homework Solutions 384

# Pre-Calc Homework Solutions 384 - 384 Section 9.4 an an(n 1...

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30. lim n ) } a a n 1 n 1 } ) 5 lim n 5 lim n ( n 1 1) ) x 2 4 ) 5 ‘ ( x 4) The series converges only for x 5 4, so the radius of convergence is 0. 31. lim n ) } a a n 1 n 1 } ) 5 lim n 5 lim n 2 ) x 2 1 ) 5 2 ) x 2 1 ) The series converges for ) x 2 1 ) , } 1 2 } and diverges for ) x 2 1 ) . } 1 2 } , so the radius of convergence is } 1 2 } . 32. lim n ) } a a n 1 n 1 } ) 5 lim n } ) 4 ( x n 2 1 5 1 ) 2 ) 3 n / 1 2 3 } ? } ) 4 x 2 n 3 5 /2 ) 2 n 1 1 } 5 lim n (4 x 2 5) 2 5 (4 x 2 5) 2 The series converges for (4 x 2 5) 2 , 1, which is equivalent to ) 4 x 2 5 ) , 1, or ) x 2 } 5 4 } ) , } 1 4 } and diverges for ) x 2 } 5 4 } ) . } 1 4 } . The radius of convergence is } 1 4 } . 33. lim n ) } a a n 1 n 1 } ) 5 lim n } ) x ˇ 1 n w p 1 w ) n 1 1 w 1 } ? } ) x ˇ 1 n w p ) n } 5 lim n ) x 1 p ) 5 ) x 1 p ) The series converges for ) x 1 p ) , 1 and diverges for ) x 1 p ) . 1, so the radius of convergence is 1. 34. lim n ) } a a n 1 n 1 } ) 5 lim n } ) x 2 2 ˇ n 1 2 w 1 ) 2 n 1 3 } ? } ) x 2 ˇ 2 n 2 w ) 2 n 1 1 } 5 lim n } 1 2 } ( x 2 ˇ 2 w ) 2 5 } 1 2 } ( x 2 ˇ 2 w ) 2 The series converges for } 1 2 } ( x 2 ˇ 2 w )
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