How can I determine the interval of convergence for a power series using the ratio test?

To determine the interval of convergence for a power series using the ratio test, you follow these steps: Given a power series ∑a_n(x-c)^n, apply the ratio test by calculating the limit L = lim (n→∞) |a_(n+1)/a_n|. If L < 1, the series converges absolutely. If L > 1, it diverges. If L = 1, the test is inconclusive. The radius of convergence R is 1/L. The interval of convergence is then (c-R, c+R). Check the endpoints separately to determine if they are included in the interval.

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