Example 2: Interval of Convergence (Half-open)

Find the interval of convergence of

We compute the limit

By the Ratio Test the series converges for |x| < 1 and diverges for |x| > 1, so the radius of convergence is r = 1.

At x = 1 the series is

which is divergent. At x = -1 the series is

which converges by the Alternating Series Test. The interval of convergence is [-1,1).