Creative proofs in combinations

In this article, we present four issues and provide a creative and concise proof for each of them. The four issues are: 1- Inequality $\frac{1}{\sqrt{nπ+\fracπ{2}}}<\frac{\binom{2n}{n}}{2^{2n}}<\frac{1}{\sqrt{nπ}}$ 2- A special case of Jonathan Wilde's problem 3- Combination series 4- A feature of powerful numbers.

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