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Question Number 162411 by HongKing last updated on 29/Dec/21

$$\mathrm{Prove}\mathrm{the}\mathrm{identity}\mathrm{for}\mathrm{any}{}^{\prime }{\mathbf{n}}^{\prime }\mathrm{in}\mathrm{Real}\mathrm{number}$$$$\left[\frac{\mathrm{n}}{2}\right]\cdot \left[\frac{\mathrm{n}+1}{2}\right]=\frac{1}{4}({\left[\mathrm{n}\right]}^2+2\left[\frac{\mathrm{n}}{2}\right]-\left[\mathrm{n}\right])$$$$[\ast ]\mathrm{Greatest}\mathrm{Integer}\mathrm{Function}$$

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