The sum $\sum_{\mathrm{r}=0}^{10}{ }^{20} \mathrm{C}_{\mathrm{r}}$ is equal to

Question

Professor PC Thomas Classes · Answer

Sum of half binomial coefficients: $\sum_{r=0}^{10} { }^{20}C_r = \frac{2^{20} + { }^{20}C_{10}}{2} = 2^{19} + \frac{1}{2}{ }^{20}C_{10}$.