How do you test a power series for convergence?
Since the convergence of a power series depend on the value of
Here is an example.
The interval of convergence of a power series is the set of all x-values for which the power series converges.
Let us find the interval of convergence of
By Ratio Test,
which means that the power series converges at least on
Now, we need to check its convergence at the endpoints:
which is convergent. So,
which is divergent. So,
Hence, the interval of convergence is