Chứng minh: $C_{2013}^{0}C_{2013}^{1000}-C_{2013}^{1}C_{2013}^{999}+C_{2013}^{2}C_{2013}^{9 98}+...+(-1)^{k}C_{2013}^{k}C_{2013}^{1000-k}+...+C_{2013}^{1000}C_{2013}^{0}=C_{2013}^{500}$