Determine the radius of Convergence of this telescoping series Can anyone point it out how to find the radius of convergence of this series? 
$\sum_{n= 1}^{\infty}\dfrac{1}{(x+n) \cdot (x+n - 1)}$ 
I tried the Ratio Test, but the limit goes to 1.
Any help is appreciated, thank you :)

This can be rewritten as:
$$\sum_{n=1}^{\infty} \left(\frac{1}{x+n}-\frac{1}{x+n+1}\right)=\frac{1}{x+1}$$
Since it's a telescopic series and not a power one, this is always convergent (for every real $x \neq -1$).
As @Doug M noticed, $x$ cannot be a negative integer since the sum is not bounded.
