Interval of convergence with binomial coefficient

[jetsetjoe]

Homework Statement

Find the radius of converge of:

$$\sum$$x$$^{}(n choose k)$$

Homework Equations

Radius of converge = 1/limsup|an+1/an|, for power series: anx^n

The Attempt at a Solution

Tried rewriting (n choose k) as: n!/[k!(n-k)!]

but where do I go from here? How do I take out x^n?

 

[Kummer]

How is the series defined?
Is it,
$$\sum_{n=k}^{\infty} x^{{n\choose k}}$$


For example,
$$\sum_{n=0}^{\infty} x^{n!}$$
Use the ratio test.