> 
> Is function 
>  $$f(x) = \frac 1 x - \frac 1 {x+1} + \frac{1}{x+2} - \frac 1{x+3} + \cdots$$
>  continuous on $(0, \infty)$ ?
> 
> 
> 

I think I should extend the continuity of each term to $f$ but I cannot show that series converges uniformly.