The binomial series is .

can be written as .

Binomial series is

.

Find the radius of convergence.

The series is the standard binomial series, so this will converge when or .

The ratio test states that :

(1) If   then the series converges absolutely.

(2) If  then the series does not converge.

(3) If or the limit fails to exist then the test is inclusive.

Therefore the result is same, converges if , therefore .

and .