Let C_r denote the binomial coefficient of x^r in the expansion of (1+x)^10. If for α, β ∈ R, C_1+3 · 2 C_2+5 · 3 C_3+… upto 10 terms =(α ×…

Let $\displaystyle \mathrm{C}_{\mathrm{r}}$ denote the binomial coefficient of $\displaystyle x^{\mathrm{r}}$ in the expansion of $\displaystyle (1+x)^{10}$. If for $\displaystyle \alpha, \beta \in \mathbf{R}$, $\displaystyle C_1+3 \cdot 2 C_2+5 \cdot 3 C_3+\ldots$ upto $\displaystyle 10$ terms $\displaystyle =\frac{\alpha \times 2^{11}}{2^\beta-1}\left(C_0+\frac{C_1}{2}+\frac{C_2}{3}+\ldots\right.$ upto $\displaystyle 10$ terms $\displaystyle )$ then the value of $\displaystyle \alpha+\beta$ is equal to \_\_\_\_.