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
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text: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)" Ö
-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
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