Question

Chứng minh : 1/2!+1/3!+1/4!+...+1/2023!<1

Answer 1

Lời giải:

$\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+...+\frac{1}{2023!}$

$< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{2022.2023}$

$=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{2023-2022}{2022.2023}$

$< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{2022}-\frac{1}{2023}$

$=1-\frac{1}{2023}<1$

 Ta có đpcm