How to find $ \lim_{n \to \infty}\prod_{i=0}^{n}\frac {qn+ip+1}{qn+ip}$?
Evaluate $\lim_{n\to\infty}\frac {qn+1}{qn} \frac {qn+p+1}{qn+p} \cdots \frac {qn+np+1}{qn+np}$ where $p\in\mathbb{N}\setminus\{0,1\},q>0.$