Given the power series n = 0 Find the Integral of the Power Series. 00 2 A, x2" dx = E A x(2n - 1) A n = 0 n = 0 00 00 B. Σ Α, x (2n - 1) .2n dx A n = 0 n = 0 x (2n + 1) Σ. 00 A 2n dx = n =0 2n 00 x(2n + 1) 00 D) ΣΑ, 2n dx = n = 0 n = 0 2n + 1 00 00 E x2" dx = E A (2n – 1) x(2n - 1) n = 0 n = 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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q14

Given the power series
00
2 A x2"
n = 0
Find the Integral of the Power Series.
Σ
00
A
x2" dx = 2 A
x (2n - 1)
n = 0
n = 0
Σ
B
.2n
dx = 2 A
2n x(2n - 1)
A
n = 0
n = 0
00
(2n + 1)
E A,
2n
A.
n = 0
dx =
n = 0
2n
00
x (2n
|dx = 2 A
+ 1)
00
E A,
n = 0
n = 0
2n + 1
00
E
dx =Σ Α
A (2n – 1) x(2n - 1)
n = 0
n = 0
Transcribed Image Text:Given the power series 00 2 A x2" n = 0 Find the Integral of the Power Series. Σ 00 A x2" dx = 2 A x (2n - 1) n = 0 n = 0 Σ B .2n dx = 2 A 2n x(2n - 1) A n = 0 n = 0 00 (2n + 1) E A, 2n A. n = 0 dx = n = 0 2n 00 x (2n |dx = 2 A + 1) 00 E A, n = 0 n = 0 2n + 1 00 E dx =Σ Α A (2n – 1) x(2n - 1) n = 0 n = 0
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