Question

chung minh rang 1/20.23 +1/23+26 +1/26.29+...+1/77.80<1/9

giup minh nhe mai nop roi

Answer 1

ko bt sory nha

Answer 2

Ta có:

\(\frac{1}{20.23}+\frac{1}{23.26}+\frac{1}{26.29}+...+\frac{1}{77.80}\)

\(=\frac{1}{3}.\left(\frac{3}{20.23}+\frac{3}{23.26}+\frac{3}{26.29}+...+\frac{3}{77.80}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+\frac{1}{26}-\frac{1}{29}+...+\frac{1}{77}-\frac{1}{80}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{20}-\frac{1}{80}\right)\)

\(=\frac{1}{3}.\frac{3}{80}\)

\(=\frac{1}{80}\)

Mà \(\frac{1}{80}< \frac{1}{9}\)

\(\Rightarrow\frac{1}{20.23}+\frac{1}{23.26}+\frac{1}{26.29}+...+\frac{1}{77.80}< \frac{1}{9}\left(đpcm\right)\)

Học tốt 

Answer 3

CMR:\(\frac{1}{20.23}+\frac{1}{23.26}+\frac{1}{26.29}+....+\frac{1}{77.80}< \)\(\frac{1}{9}\)

Ta gọi A= \(\frac{1}{20.23}+\frac{1}{23.26}+\frac{1}{26.29}+...+\frac{1}{77.80}\)

Khi đó ta có:

\(3A=\frac{3}{20.23}+\frac{3}{23.26}+\frac{3}{26.29}+...+\frac{3}{77.80}\)

A= \([(\frac{1}{20}-\frac{1}{23})+(\frac{1}{23}-\frac{1}{26})+(\frac{1}{26}-\frac{1}{29})+....+(\frac{1}{77}-\frac{1}{80}]\)

A=\(\frac{1}{20}-\frac{1}{80}\)

A=\(\frac{3}{80}\)

\(\Rightarrow\)A=\(\frac{1}{80}\)

So sánh:  \(\frac{1}{80}< \frac{1}{9}\)(ĐPCM)

Answer 4

Câu kết cậu làm giống bạn Nguyễn Hải Nam nha, cách bạn ấy đơn giản hơn