K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

28 tháng 5 2018

\(\Rightarrow\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{42}\cdot\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{42}\cdot\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{6}+\frac{1}{42}\cdot\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\frac{1}{3}+\frac{1}{42}\cdot\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\frac{1}{42}\cdot\frac{x}{3}=\frac{5}{21}-\frac{1}{3}\)

\(\Rightarrow\frac{1}{42}\cdot\frac{x}{3}=\frac{-2}{21}\)

\(\Rightarrow\frac{x}{3}=\frac{-2}{21}\div\frac{1}{42}\)

\(\Rightarrow\frac{x}{3}=-4\)

\(\Rightarrow\frac{x}{3}=\frac{-12}{3}\)

\(\Rightarrow x=-12\)

26 tháng 9 2020

 \(x+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}=\frac{47}{42}\)

\(x+\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)=\frac{47}{42}\)

\(x+A=\frac{47}{42}\)

     ta thấy :

              \(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)

              \(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\)

                  \(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

               \(A=\frac{1}{1}-\frac{1}{6}\)

             \(A=\frac{5}{6}\)

       vậy \(x+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}=\frac{47}{42}\)       

  hay  \(x+\frac{5}{6}=\frac{47}{42}\)

     \(x=\frac{47}{42}-\frac{5}{6}\)

 \(x=\frac{2}{7}\)

\(x+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}=\frac{47}{42}\)

\(x=\frac{47}{42}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\)

\(x=\frac{47}{42}-\frac{5}{6}\)

\(x=\frac{2}{7}.\)

27 tháng 7 2015

b ) \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}=\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)

11 tháng 6 2018

215 - 15 x { 25 - 15 : [ 3 x 45 - 3 x ( 50 - 2 x 3 ) ] }

= 215 - 15 x { 25 - 15 : [ 3 x 45 - 3 x 44 ] }

= 215 - 15 x { 25 - 15 : 3 }

= 215 - 15 x 20

= 215 - 300

= -85

b) \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)

11 tháng 3 2018

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

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

\(=\frac{6}{7}\)

11 tháng 3 2018

1/2+1/6+1/12+1/20+1/30+1/42

=1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+1/6×7

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

=1-1/7

=6/7.

Tích mk nha

\(\frac{1}{2}\)+   \(\frac{1}{6}\)+   \(\frac{1}{12}\)\(\frac{1}{20}\)+   \(\frac{1}{30}\)+   \(\frac{1}{42}\)+    \(\frac{1}{56}\)

=   \(\frac{1}{1.2}\)+   \(\frac{1}{2.3}\)+    \(\frac{1}{3.4}\)+   \(\frac{1}{4.5}\)+   ......   +   \(\frac{1}{7.8}\)

=   \(1\)\(-\)\(\frac{1}{8}\)

=    \(\frac{7}{8}\)

thiếu bước :v

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)

\(=1-\frac{1}{8}\)

\(=\frac{7}{8}\)

11 tháng 10 2020

=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{110}\)

=\(\frac{1}{1.2}+\frac{1}{2\cdot3}+\frac{1}{3.4}+......+\frac{1}{10.11}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.......+\frac{1}{10}-\frac{1}{11}\)

=\(1-\frac{1}{11}\)

=\(\frac{10}{11}\)

11 tháng 10 2020

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{42}+...+\frac{1}{110}\)

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{10\cdot11}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{10}-\frac{1}{11}\)

\(=1-\frac{1}{11}\)

\(=\frac{10}{11}\)

19 tháng 1 2016

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

\(\Leftrightarrow\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{7\cdot8}\)

\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{8}\)

\(\Leftrightarrow1-\frac{1}{8}\)

\(\Leftrightarrow\frac{7}{8}\)

19 tháng 1 2016

Đặt A=1/2+1/6+1/12+....+1/56                                                                                                                               A=1/1*2+1/2*3+1/3*4+.....+1/7*8                                                                                                                     A=1-1/2+1/2-1/3+1/3-1/4+..........+1/7-1/8                                                                                                        A=1-1/8                                                                                                                                                         A=7/8 , tích nha 

18 tháng 10 2015

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{90}+\frac{1}{110}\)

\(=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+...+\frac{1}{9\times10}+\frac{1}{10\times11}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{2}-\frac{1}{11}=\frac{11}{22}-\frac{2}{22}=\frac{9}{22}\)

18 tháng 10 2015

1/6 + 1/12 + 1/20 + ... + 1/110

= 1/2.3 + 1/3.4 + 1/4.5 + ... + 1/10.11

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/10 - 1/11

= 1/2 - 1/11

= 9/22