Question

[Nguyễn Đoàn Nam Khánh]

S =1 / 21 + 1/ 22 + 1/ 23 + ... + 1/149 + 1/150 

Hãy so sánh S với 5/4

Nhanh nha!

Answer 1

[Bảo Ngọc]

Sửa đề: $S=\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+...+\frac{1}{50}$

Ta có: $S=\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+...+\frac{1}{50}$

$=\frac{1}{20}+\left(\frac{1}{21}+\frac{1}{22}+...+\frac{1}{30}\right)+\left(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{40}\right)+\left(\frac{1}{41}+\frac{1}{42}+...+\frac{1}{50}\right)$

$\iff S>\frac{1}{20}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{1}{4}+\frac{1}{3}+\frac{1}{4}$

$\iff S<=\frac{5}{4}$(đpcm)