# Finding $a$ and $r$ such that $\lim\limits_{n\to \infty} n^r \cdot \frac12 \cdot \frac34 \cdots \frac{2n-1}{2n}=a$

Find $a,r>0$ such that

$$\lim_{n\to \infty} n^r \cdot \frac12 \cdot \frac34 \cdots \frac{2n-1}{2n}=a$$

I don't have any idea to solve it. How can I solve it?

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