Câu hỏi của NGUYỄN HẢI ANH

Question

Rút gọn biểu thức:

$A=-\dfrac{2}{1\cdot3}-\dfrac{2}{3\cdot5}-\dfrac{2}{5\cdot7}-...-\dfrac{2}{19\cdot21}-\dfrac{2}{23\cdot25}-\dfrac{2}{25\cdot27}-\dfrac{1}{27}$

ta được A = ...

GIÚP MÌNH VỚI, MÌ...

ngonhuminh · Accepted Answer

$A=-B$

$B=\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{23.25}+\dfrac{2}{25.27}+\dfrac{1}{27}$

$B=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{23}-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}$

$B=1$

A=-1Câu trả lời: $A=-B$

$B=\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{23.25}+\dfrac{2}{25.27}+\dfrac{1}{27}$

$B=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{23}-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}$

$B=1$

A=-1

Bùi Bảo Châu · Answer

$A=-\dfrac{2}{1.3}-\dfrac{2}{3.5}-......-\dfrac{2}{25.27}-\dfrac{1}{27}$

$\Leftrightarrow A=-\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+.....+\dfrac{1}{27}\right)$

$\Leftrightarrow A=-\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}\right)$

$\Leftrightarrow A=-1$Câu trả lời: $A=-\dfrac{2}{1.3}-\dfrac{2}{3.5}-......-\dfrac{2}{25.27}-\dfrac{1}{27}$

$\Leftrightarrow A=-\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+.....+\dfrac{1}{27}\right)$

$\Leftrightarrow A=-\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}\right)$

$\Leftrightarrow A=-1$

Kudo Shinichi · Answer

= -(1-1/3+1/3-1/5+1/5-1/7+..+1/19-1/21+1/21-1/23+1/23-1/25+1/25-1/27+1/27)

= -1Câu trả lời: = -(1-1/3+1/3-1/5+1/5-1/7+..+1/19-1/21+1/21-1/23+1/23-1/25+1/25-1/27+1/27)

= -1

Violympic toán 6