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4 tháng 6 2018

Đặt A = \(1\frac{1}{6}+1\frac{1}{12}+1\frac{1}{20}+1\frac{1}{30}+...+1\frac{1}{9900}\)

=> A = \(1+\frac{1}{6}+1+\frac{1}{12}+1+\frac{1}{20}+1+\frac{1}{30}+...+1+\frac{1}{9900}\)

=> A = \(\left(1+1+1+1+...+1\right)+\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\right)\)

=> A = \(\left(1+1+1+1+...+1\right)+\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\right)\)

=> A = \(99+\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\right)\)

=> A = \(99+\left(\frac{1}{2}-\frac{1}{100}\right)\)

=> A = \(99+\frac{49}{100}\)

=> A = \(\frac{9949}{100}\)

11 tháng 3 2016

T là 99/100 . Đúng 100% luôn nhé .

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

12 tháng 10 2016

tôi bị sai sô \(\frac{1}{110}\)nha mọi  người thông cảm

12 tháng 10 2016

3581/3960 nha bn

K mình nha

28 tháng 5 2018

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

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

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

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

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

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

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

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

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

\(\Rightarrow x=-12\)