怪我太菜，啥也不会

第一题：求$\dfrac{2}{1\times(1+2)}+\dfrac{3}{(1+2)\times(1+2+3)}+\cdots+\dfrac{100}{(1+2+\cdots +99)\times(1+2+\cdots +100)}$

第二题：证明$\dfrac{1}{1\times99}+\dfrac{1}{3\times97}+\cdots+\dfrac{1}{99\times1}=\dfrac{1}{50}\times(1+\dfrac{1}{3}+\cdots+\dfrac{1}{99})$

第三题：证明$\dfrac{4}{3}\times\dfrac{10}{9}\times\dfrac{28}{27}\times\cdots\times\dfrac{3^{2021}+1}{3^{2021}}<2$

打LaTeX好累啊...