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