$\prod_{i=1}^n (i+n)$ - To what does it converges?

Question

I try to prove that $\sum^n_{k=0} {n\choose k}^2 = {2n \choose n} $, but a given moment during the proof, I am faced with the product $\prod_{i=1}^n (i+n)$ that I am not able to solve. Does someone could tell me how to converge the equation?

Answer 1

Notice that

$$\prod_{i=1}^n(i+n)=(1+n)(2+n)\cdots(2n)\ge n\xrightarrow{n\to\infty}\infty$$