The binomial series is .

The binomial series can be written as .

Binomial series is

.

Now find the radius of convergence,using the ratio test

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 inconclusive. 

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Therefore the series converges if , therefore .

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and .

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