= 5-2/2x5+8-5/5x8+11-8/8x11+14-11/11x14

=(1/2-1/5)+(1/5-1/8)+(1/8-1/11)+(1/11-1/14)

=(1/2+1/5+1/8+1/11)-(1/5+1/8+1/11+1/14)

=1/2-1/14

=3/7

Vậy B=3/7

B = 3/2x5 + 3/5x8 + 3/8x11 + 3/11x14

B = 1/2 - 1/5 + 1/5 - 1/8 + ..... + 1/14 - 1/17

B = 1/2 - 1/17

B = 15/34

B= \(\frac{3}{2}\)- \(\frac{3}{5}\) + \(\frac{3}{5}\)- \(\frac{3}{8}\)+ \(\frac{3}{8}\)- \(\frac{3}{11}\)+ \(\frac{3}{11}\)+ \(\frac{3}{14}\)

  =\(\frac{3}{2}\)- \(\frac{3}{14}\)

  = \(\frac{9}{7}\)

Đặt \(A=\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}\)

\(A=\dfrac{3}{2}-\dfrac{3}{5}+\dfrac{3}{5}-\dfrac{3}{8}+\dfrac{3}{8}-\dfrac{3}{11}+\dfrac{3}{11}-\dfrac{3}{14}\)

\(A=\dfrac{3}{2}-\dfrac{3}{14}\)

\(A=\dfrac{21}{14}-\dfrac{3}{14}\)

\(A=\dfrac{18}{14}\)

\(A=\dfrac{9}{7}\)

\(A=1\dfrac{2}{7}\)

\(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+\dfrac{3}{11\cdot14}\\ =\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}\\ =\dfrac{1}{2}-\dfrac{1}{14}\\ =\dfrac{3}{7}\)

Xin lỗi mình sửa lại

Đặt \(A=\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+\dfrac{3}{11.14}\)

\(A=\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}\)

\(A=\dfrac{1}{2}-\dfrac{1}{14}\)

\(A=\dfrac{7}{14}-\dfrac{1}{14}\)

\(A=\dfrac{6}{14}=\dfrac{3}{7}\)

A = \(\dfrac{1}{2}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{8}\) + \(\dfrac{1}{8}\) - \(\dfrac{1}{11}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{14}\) + \(\dfrac{1}{14}\) - \(\dfrac{1}{17}\) + \(\dfrac{1}{17}\) - \(\dfrac{1}{20}\)
   = \(\dfrac{1}{2}\) - \(\dfrac{1}{20}\)
   = \(\dfrac{9}{20}\)

cách làm như trên

=9/20

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)

\(=\frac{1}{2}-\frac{1}{14}\)

\(=\frac{7}{14}-\frac{1}{14}\)

\(=\frac{6}{14}\)

\(=\frac{3}{7}\)

3/2x5 + 3/5x8 + 3/8x11 + 3/11x14 

= 3/2 - 3/5 + 3/5 - 3/8 + 3/8 - 3/11 + 3/11 - 3/14 

= 3/2 - 3/14 

= 21/14 - 3/14 

= 18/14 

= 9/5 

\(B=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}=\frac{1}{2}-\frac{1}{14}=\frac{3}{7}\)

\(A=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}.\)

\(A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\)

\(A=\frac{1}{2}-\frac{1}{20}\)

\(A=\frac{10}{20}-\frac{1}{20}\)

\(A=\frac{9}{20}\)

Mình ra kết quả thứ nhất là 17/60 thứ 2 là 9/20 các bạn thấy cái nào đúng 

Ta có : A=3/2x5+3/5x8+3/8x11+3/11x14+3/14x17+3/17x20

     => A=1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20

     => A=1/2-1/20

     => A=9/20

Vậy A=9/20

Hãy ủng hộ mik nha bạn .

Ta có: \(\frac{3x}{2\cdot5}+\frac{3x}{5\cdot8}+\frac{3x}{8\cdot11}+\frac{3x}{11\cdot14}=\frac{1}{21}\)

\(\Leftrightarrow x\cdot\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}\right)=\frac{1}{21}\)

\(\Leftrightarrow x\cdot\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\right)=\frac{1}{21}\)

\(\Leftrightarrow x\cdot\left(\frac{1}{2}-\frac{1}{14}\right)=\frac{1}{21}\)

\(\Leftrightarrow x\cdot\frac{3}{7}=\frac{1}{21}\)

\(\Leftrightarrow x=\frac{1}{21}:\frac{3}{7}=\frac{1}{21}\cdot\frac{7}{3}=\frac{7}{63}=\frac{1}{9}\)

Vậy: \(x=\frac{1}{9}\)

A=1/5-1/8+1/8-1/11+...+1/602-1/605

=1/5-1/605

=24/121

\(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{2006.2009}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{2006}-\frac{1}{2009}\)

\(=\frac{1}{5}-\frac{1}{2009}\)

\(=\frac{2004}{10045}\)

Đề: Tính

\(A=\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{2006.2009}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{2006}-\frac{1}{2009}\)

\(=\frac{1}{5}-\frac{1}{2009}=\frac{2004}{10045}\)

Vậy \(A=\frac{2004}{10045}.\)

\(A=\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+....+\frac{3}{2006\times2009}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+.......+\frac{1}{2006}-\frac{1}{2009}\)

\(=\frac{1}{5}-\frac{1}{2009}\)

\(=\frac{2009}{10045}-\frac{5}{10045}\)

\(=\frac{2004}{10045}\)

Chúc bạn học tốt

\(\dfrac{x}{2\times5}+\dfrac{x}{5\times8}+\dfrac{x}{8\times11}+\dfrac{x}{11\times14}+...+\dfrac{x}{32\times35}=\dfrac{33}{70}\)

\(\dfrac{x}{3}\cdot\left(\dfrac{3}{2\times5}+\dfrac{3}{5\times8}+\dfrac{3}{8\times11}+\dfrac{3}{11\times14}+...+\dfrac{3}{32\times35}\right)=\dfrac{33}{70}\)

\(\dfrac{x}{3}\cdot\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+...+\dfrac{1}{32}-\dfrac{1}{35}\right)=\dfrac{33}{70}\)

\(\dfrac{x}{3}\cdot\left(\dfrac{1}{2}-\dfrac{1}{35}\right)=\dfrac{33}{70}\)

\(\dfrac{x}{3}\cdot\dfrac{33}{70}=\dfrac{33}{70}\)

\(\dfrac{x}{3}=\dfrac{33}{70}:\dfrac{33}{70}\)

\(\dfrac{x}{3}=1\)

\(x=3\)