What is the interval of convergence of $sum_1^oo ((3x-2)^2)/(nx3^n)$ ?

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What is the interval of convergence of $sum_1^oo ((3x-2)^2)/(nx3^n)$ ?

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Answer 1 · 2016-05-29T09:54:05

Is convergent for all $x ne 0$

Explanation:

This power series is equivalent to
$(3x-2)^2/x sum_{n=1}^{infty}1/(i 3^i)$ . The sum $sum_{n=1}^{infty}1/(i 3^i)$ is convergent to a real number $C_0$ so the power series is
equivalent to $C_0 (3x-2)^2/x$ which is convergent for all $x ne 0$

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What is the interval of convergence of $sum_1^oo ((3x-2)^2)/(nx3^n)$ ?

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