The set of all values of $$\(x\)$$ for which $$\(\sum_{n=1}^{\infty} \frac{n \cdot 2^{n}}{x^{n}}\)$$ converges is

A.
only \(x=0\)
B.
\(-2< x< 2\)
C.
\(|x|> 2\)
D.
\(|x| \geq 2\)
Calculus
AP
College Board
Exam No:AP Calculus Unit 10 Questions Set Year:2024 Question No:36

Answer:

C

Knowledge points:

10.1 Defining Convergent and Divergent Infinite Series
10.13 Radius and Interval of Convergence of Power Series

Solution:

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