# Interval of convergence

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I am trying to find the interval of convergence for the attached power series (attached as a gif). I am also supposed to check the endpoints for convergence. I'm not that good with power series and the format of this power series is really throwing me off. So I am looking for the steps to find the interval of convergence (also checking the end points).

Â© BrainMass Inc. brainmass.com March 6, 2023, 12:43 pm ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/interval-convergence-power-series-5510

#### Solution Preview

An automatic response to a power series of this type is to use the ratio test. In the ratio test, you want to look at the limit as n goes to infinity of the absolute value of a_n+1 / a_n:

lim |a_n+1|

n->inf --------

| ...

#### Solution Summary

This provides the steps to find the interval of convergence (also checking the end points).

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