Q3) Find the Radius and Interval of Convergence for each of the following power series. (a) n=1 (2n)!(x-5)" n₁ 30 (b) n=1 (x+2)n (-5)"√n n = 1 (2n)! (x-5)" 130 Ratio Test 1im 1-200 Tim 1-700 lim 4-300 antl ап -n+1 2(n+1)! (x-5) 30+1 26)! (x+5)" n30 Center at x=5 (+1)/(x-x11 n=1 (x+2)" (-5)"√n Center at x=-2. Root Test lim lan l h //n (x+2) 1-20 Tim 1-2005)√n 30 Tim= 1x+21 n-x * (At! (x+5)* (n³30+1) (n+1)430 (x-51 Tim 1-∞ lim 31 (n+1) 1x-51 11-1700 1x-5101<1 to Converge only true at x=5 ROC is o IOC is X=5 -5 n (x+2( lim - 5 (nik) k -5(1)1 1x+2/1im 1x+21 1-700-5(1)42 . 1x+21 > -5 <1 to Converge Roc is -5 IOC is -7, 3 Test End point D (-5)" n=1 (-5)" √ñ -5<8+2<5 Test Endpoint Σ (5)" مح n=1 Diverge as a p-series n=1 (-5) √n n=1 (-1) Converge by Ast

Q3) Find the Radius and Interval of Convergence for each of the following power series. (a) n=1 (2n)!(x-5)" n₁ 30 (b) n=1 (x+2)n (-5)"√n n = 1 (2n)! (x-5)" 130 Ratio Test 1im 1-200 Tim 1-700 lim 4-300 antl ап -n+1 2(n+1)! (x-5) 30+1 26)! (x+5)" n30 Center at x=5 (+1)/(x-x11 n=1 (x+2)" (-5)"√n Center at x=-2. Root Test lim lan l h //n (x+2) 1-20 Tim 1-2005)√n 30 Tim= 1x+21 n-x * (At! (x+5)* (n³30+1) (n+1)430 (x-51 Tim 1-∞ lim 31 (n+1) 1x-51 11-1700 1x-5101<1 to Converge only true at x=5 ROC is o IOC is X=5 -5 n (x+2( lim - 5 (nik) k -5(1)1 1x+2/1im 1x+21 1-700-5(1)42 . 1x+21 > -5 <1 to Converge Roc is -5 IOC is -7, 3 Test End point D (-5)" n=1 (-5)" √ñ -5<8+2<5 Test Endpoint Σ (5)" مح n=1 Diverge as a p-series n=1 (-5) √n n=1 (-1) Converge by Ast

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.4: Series And Their Notations

Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+

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