Does $\lim_{n\rightarrow\infty} (\frac{1}{n+a} + \frac{1}{n+2a} + \cdots + \frac{1}{n+na}) $ converge? I want to check whether 
$\lim_{n\rightarrow\infty} (\frac{1}{n+a} + \frac{1}{n+2a} + \cdots + \frac{1}{n+na}) $ 
converges or not. (a is a positive constant number.)
If it converges, how to find the value it converges?
And if not, why?

This is the limit of a Riemann sum:
$$\lim_{n\rightarrow\infty} (\frac{1}{n+a} + \frac{1}{n+2a} + \cdots + \frac{1}{n+na})=\frac{1}{a}\lim_{n\rightarrow\infty}\frac{a}{n}\sum_{k=1}^n\frac{1}{1+\frac{ka}{n}}\\=\frac{1}{a}\int_0^a\frac{dx}{1+x}=\frac{\ln(a+1)}{a}.$$
