# Interval of convergence with binomial coefficient

1. Jul 15, 2007

### jetsetjoe

1. The problem statement, all variables and given/known data

Find the radius of converge of:

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

2. Relevant equations

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

3. 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?

2. Jul 15, 2007

### 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.