I am working with power series and this answer explanation shown in the screen shot does not make sense to me. Why and are they reindexing and how to they get that resulting answer? (- 1)k + 1 1 0k- 1 kx2k-1 = 0 +x -20x3 300x5 -40000x7 + ...in its expandedThe power series for g(x) isk 0form. Drop the zero term and re-index the series so that k 0 corresponds to the term x0og(x)>(-1)k10K (k+ 1)x2k+1k 0

Name: I am working with power series and this answer explanation shown in th
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Description: I am working with power series and this answer explanation shown in the screen shot does not make sense to me. Why and are they reindexing and how to they get that resulting answer? (- 1)k + 1 1 0k- 1 kx2k-1 = 0 +x -20x3 300x5 -40000x7 + ...in its ex

Answered: (- 1)k + 1 1 0k- 1 kx2k-1 = 0 +x -20x3…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

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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I am working with power series and this answer explanation shown in the screen shot does not make sense to me. Why and are they reindexing and how to they get that resulting answer?

(- 1)k + 1 1 0k- 1 kx2k-1 = 0 +x -20x3 300x5 -40000x7 + ...
in its expanded
The power series for g(x) is
k 0
form. Drop the zero term and re-index the series so that k 0 corresponds to the term x
0o
g(x)>(-1)k10K (k+ 1)x2k+1
k 0

Expert Solution

Step 1

Note that the variable k lies inside the summation as a product terms. So, when k = 0, the first term of the series becomes zero.

Σ-)0 ke- (-1)** 10*' (0) >20 Σ-1)"
k+1
= (-1)'10-1(0)x20)-1
2k-1
Σ-1)"10*" kκ.
k-0
k-1
k+1
-1x10' x 0x x1 +1)10-1 κ
2k-1
k1
k+1
0(-1) 10*-1kx2*-1
k1
k+1
-Σ-1)104" kλ-
Ε
k-1

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