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[TEX]\frac{C_{n}^{0}}{C_{n+2}^{1}}+\frac{C_{n}^{1}}{C_{n+3}^{2}}+\frac{C_{n}^{2}}{C_{n+4}^{3}}+....+\frac{C_{n}^{k}}{C_{n+k+2}^{k+1}}+......+\frac{C_{n}^{n}}{C_{2n+2}^{n+1}}=\frac{1}{2}[/TEX]
[TEX]\frac{C_{n}^{0}}{C_{n+2}^{1}}+\frac{C_{n}^{1}}{C_{n+3}^{2}}+\frac{C_{n}^{2}}{C_{n+4}^{3}}+....+\frac{C_{n}^{k}}{C_{n+k+2}^{k+1}}+......+\frac{C_{n}^{n}}{C_{2n+2}^{n+1}}=\frac{1}{2}[/TEX]