Đáp án + Giải thích các bước giải:
`\frac{1}{2!}+\frac{2}{3!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}`
`=\frac{2-1}{2!}+\frac{3-1}{3!}+\frac{4-1}{3!}+...+\frac{100-1}{100!}`
`=\frac{2}{2!}-\frac{1}{2!}+\frac{3}{3!}-\frac{1}{3!}+\frac{4}{4!}+...+\frac{100}{100!}-\frac{1}{100!}`
`=\frac{1}{1!}-\frac{1}{2!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{3!}-\frac{1}{4!}+..+\frac{1}{99!}-\frac{1}{100!}`
`=1-\frac{1}{100}<1`
`text{#Study Well}`
