Use the power series f(x) = In (1-x) = -Σ, for - 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the power series f(x) = In (1-x) = -
k=1
function (centered at 0). Give the interval of convergence of the new series.
f(7x)= In (1-7x)
O A. ∞
Which of the following is the power series representation for f(7x)?
C.
Σ In (1-(7x)*)
k=1
-
∞
k=1
-, for 1 ≤x< 1, to find the power series representation for the following
k
(7x)k
k
B.
O D.
The interval of convergence is.
(Simplify your answer. Type your answer in interval notation.)
IM8 M8
k=1
· Σ
k=1
7k
X'
k
7xk
k
Transcribed Image Text:Use the power series f(x) = In (1-x) = - k=1 function (centered at 0). Give the interval of convergence of the new series. f(7x)= In (1-7x) O A. ∞ Which of the following is the power series representation for f(7x)? C. Σ In (1-(7x)*) k=1 - ∞ k=1 -, for 1 ≤x< 1, to find the power series representation for the following k (7x)k k B. O D. The interval of convergence is. (Simplify your answer. Type your answer in interval notation.) IM8 M8 k=1 · Σ k=1 7k X' k 7xk k
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