\(\frac{1}{2\times5}+\frac{1}{5\times8}+\frac{1}{8\times11}+\frac{1}{11\times14}+\frac{1}{14\times17}+\frac{1}{17\times20}\)

\(=\frac{1}{3}\times\left(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}+\frac{3}{17\times20}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=\frac{1}{3}\times\frac{9}{20}\)

\(=\frac{3}{20}\)

_Chúc bạn học tốt_

Đặt \(A=\frac{1}{2x5}+\frac{1}{5x8}+..+\frac{1}{17x20}\)

\(3xA=3x\left(\frac{1}{2x5}+\frac{1}{5x8}+...+\frac{1}{17x20}\right)\)

\(3xA=\frac{3}{2x5}+\frac{3}{5x8}+....+\frac{3}{17x20}\)

\(3xA=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+..+\frac{1}{17}-\frac{1}{20}\)

\(3xA=\frac{1}{2}-\frac{1}{20}\)

\(3xA=\frac{9}{20}\)

\(\Rightarrow A=\frac{3}{20}\)

lên mạng mà tra

giúp em với ạ

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

đó

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

  =\(\frac{3}{2}\)- \(\frac{3}{14}\)

  = \(\frac{9}{7}\)

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ta co 01234

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

toán 6 hả

X3 lên nhé

X3 lên

nhân cả tử và mẫu cho 3 là làm đc thôi

= 2 x ( 1/2 x 5 + 1/ 5 x 8 + 1/ 8 x 11 + 1/ 11 x 14 + 1/ 14 x 17 )

= 2 x ( 1/2 - 1/5 + 1/5 - 1/8 + ....+1/14 - 1/17)

= 2 x (1/2 - 1/17)

= 2 x 15/34

= 15/17

ĐÚNG THÌ TÍCH CHO MÌNH NHA

CHÚC BẠN HỌC GIỎI

Đặt \(A=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)

\(A=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{17}\right)\)

\(A=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{17}\right)\)

\(A=\frac{2}{3}\cdot\frac{15}{34}=\frac{5}{17}\Rightarrow A< 1\)

   \(\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)

\(=\frac{2}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\right)\)

\(=\frac{2}{3}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\right)\)

\(=\frac{2}{3}.\left(1-\frac{1}{17}\right)\)

\(=\frac{2}{3}.\frac{16}{17}\)

\(=\frac{32}{51}< \frac{51}{51}=1\)

\(\Rightarrow\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}< 1\)