Given the power series 2 (-1)" x" n = 0 Find the Derivative of the Power Series. x (n + 1) d A 2 (-1)" x" = 2 (-1)" n dx n = 0 n = 0 n + 1 00 d (B) 2 (-1)" x" = En xlm - 1) dx n = 0 n = 0

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Chapter1: Functions And Models
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Given the power series
2 (-1)" x"
n = 0
Find the Derivative of the Power Series.
x(n + 1)
d
A
2 (-1)" x" = 2 (-1)" n
dx
n = 0
n = 0
n + 1
d
(B
E (-1)" x" =
-Σ χ-1)
%3D
dx
n = 0
n = 0
00
d
(-1)" x"
(% 1) (n – 1) n² x (n – 1)
dx
n = 0
n = 0
Σ
d
D)
2 (-1)" x"
2 (-1)" x(n – 1)
-
dx
n= 0
n = 0
00
00
d
E (-1)" x" =
2 (-1)" n x" - 1)
E
dx
n =0
n = 0
Transcribed Image Text:Given the power series 2 (-1)" x" n = 0 Find the Derivative of the Power Series. x(n + 1) d A 2 (-1)" x" = 2 (-1)" n dx n = 0 n = 0 n + 1 d (B E (-1)" x" = -Σ χ-1) %3D dx n = 0 n = 0 00 d (-1)" x" (% 1) (n – 1) n² x (n – 1) dx n = 0 n = 0 Σ d D) 2 (-1)" x" 2 (-1)" x(n – 1) - dx n= 0 n = 0 00 00 d E (-1)" x" = 2 (-1)" n x" - 1) E dx n =0 n = 0
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