Find a power series representation for $$\(\frac{x}{2+3 x}\)$$ and determine the interval of convergence $$\(I\)$$.
A.
\(\sum_{n=1}^{\infty} \frac{(-3)^{n}}{2^{n+1}} x^{n+1}\) with \(I=\left(-\frac{2}{3}, \frac{2}{3}\right)\)
B.
\(\sum_{n=0}^{\infty}\left(\frac{4}{3}\right)^{n} x^{n}\) with \(I=\left(-\frac{3}{4}, \frac{3}{4}\right)\)
C.
\(\sum_{n=1}^{\infty}\left(\frac{3}{2}\right)^{n} x^{n}\) with \(I=\left[-\frac{2}{3}, \frac{2}{3}\right)\)
D.
\(\sum_{n=1}^{\infty} \frac{(-3)^{n-1}}{2^{n}} x^{n}\) with \(I=\left(-\frac{2}{3}, \frac{2}{3}\right)\)
Exam No：AP Calculus Unit 10 Questions Set 2 Year：2024 Question No：27
Answer:
D
Knowledge points:
10.13 Radius and Interval of Convergence of Power Series
10.15 Representing Functions as Power Series
Solution:
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