JEE Main 202430 Jan, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002
Let \alpha=\sum_\limits{k=0}^n\left(\frac{\left({ }^n C_k\right)^2}{k+1}\right) and \beta=\sum_\limits{k=0}^{n-1}\left(\frac{{ }^n C_k{ }^n C_{k+1}}{k+2}\right) If , then equals _______.