# What is the interval of convergence of #sum {(8 x)^n}/{n^{7}} #?

The series

is absolutely convergent for

is in convergence.

Evaluate:

We can therefore draw the following conclusion:

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The interval of convergence for the series (\sum \frac{(8x)^n}{n^7}) is (-\frac{1}{8} < x \leq \frac{1}{8}).

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