Find the value of $~\lim_{n\to\infty}\sum_{k=1}^n \frac{1\cdot 3\cdot 5\cdots (2k-1)}{3\cdot 6\cdot 9\cdots 3k}~$
How to show that $1 \over \sqrt{1 - 4x} $ generates $\sum_{n=0}^\infty \binom{2n}{n}x^n $