Ta có :
\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+...+100\right)}{1\times100+2\times99+3\times98+...+100\times1}\)
\(=\frac{\left(1+1+...+1\right)+\left(2+2+..+2\right)+\left(99+99\right)+100}{1\times100+2\times99+...+100\times1}\)
\(=\frac{1\times100+2\times99+...+100\times1}{1\times100+2\times99+...+100\times1}\)
\(=1\)