计算: $\frac{1}{2}+\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{2}{4}+\frac{3}{4}\right)+\left(\frac{1}{5}+\frac{2}{5}+\frac{3}{5}\right.$ $\left.+\frac{4}{5}\right)+\cdots+\left(\frac{1}{50}+\frac{2}{50}+\cdots+\frac{48}{50}+\frac{49}{50}\right)=$ (“希望杯”全国数学邀请赛试题)