109/110+131/132+155/156

119/60+155/156

387/130

\(109\over 110 \) + \(131\over 132\) + \(155\over 156\) = (1- \(1\over 110\)) + (1- \(1\over 132\)) + (1- \(1\over 156\))

                         = (1- \(1\over 10.11\)) + (1- \(1\over 11.12\)) + (1- \(1\over12.13\))     ( . là dấu nhân )

                         =(1+1+1) - ( \(1\over 10.11\) + \(1\over 11.12\) + \(1\over12.13\))

                         = 3 - ( \(11-10\over10.11\)+ \(12 - 11 \over 11.12\)+ \(13-12\over12.13\))

                         = 3 - ( \(1\over10\) - \(1\over11\) + \(1\over11\) - \(1\over 12\) + \(1\over 12\) - \(1\over 13\))

                         = 3 - ( \(1\over10\) - \(1\over 13\))

                         = 3 - \(1\over10\) + \(1\over 13\)

                         = \(27\over 10\)+\(1\over 13\)

                         ..........tự làm tiếp.........

\(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

=\(\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}\)

=\(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)

=\(\frac{1}{5}-\frac{1}{12}=\frac{12}{60}-\frac{5}{60}=\frac{7}{60}\)

  \(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

= \(\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}\)

= \(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)

=\(\frac{1}{5}-\frac{1}{12}\)

=\(\frac{7}{60}\)

\(\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+....+\frac{1}{240}=\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+...+\frac{1}{15.16}\)

\(=\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+...+\frac{1}{15}-\frac{1}{16}=\frac{1}{7}-\frac{1}{16}=\frac{9}{112}\)

\(=\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+\frac{1}{13.14}+\frac{1}{14.15}+\frac{1}{15.16}\)

\(=\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{16}\)

\(=\frac{1}{7}-\frac{1}{16}\)

\(=\frac{9}{112}\)

Tách:

56 = 7 x 8

72 = 8 x 9

90 = 9 x 10

110 = 10 x 11

132 = 11 x 12

156 = 12 x 13

182 = 13 x 14

210 = 14 x 15

240 = 15 x 16

=> \(\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+\frac{1}{12\cdot13}+\frac{1}{13\cdot14}+\frac{1}{14\cdot15}+\frac{1}{15\cdot16}\)

Đựợc dãy sai phân, làm tiếp được

\(\frac{1}{7}-\frac{1}{16}=\frac{9}{112}\)

Vậy kết quả là \(\frac{9}{112}\)

\(\dfrac{539}{78}\)

Đáp số là 539/78 nhé

\(\dfrac{539}{78}\)

= 47/84

Dấu \(.\)là dấu nhân nhé

Ta có : 
\(B=\frac{1}{2}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

\(\Rightarrow B=\frac{1}{2}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}\)

\(\Rightarrow B=\frac{1}{2}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)

\(\Rightarrow B=\frac{1}{2}+\frac{1}{7}-\frac{1}{12}\)

\(\Rightarrow B=\frac{42}{84}+\frac{12}{84}-\frac{7}{84}\)

\(\Rightarrow B=\frac{47}{84}\)

K mik nha 

\(B=\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

\(B=\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}\)

\(B=\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)

\(B=\frac{1}{6}-\frac{1}{12}\)

\(B=\frac{1}{12}\)

_Chúc bạn học tốt_

1/20 + 1/30 + 1/42 + ... + 1/156

= 1/4.5 + 1/5.6 + 1/6.7 + .... + 1/12.13

= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/12 - 1/13

= 1/4 - 1/13

= 9/52

1/20 + 1/30 + 1/42 + ... + 1/156

= 1/4.5 + 1/5.6 + 1/6.7 + .... + 1/12.13

= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/12 - 1/13

= 1/4 - 1/13

= 9/52

A=1/5.6+1/6.7+1/7.8+1/8.9+1/9.10+1/10.11+1/11.12

A=1/5-1/12
Tự tính

\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

\(=\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}\)

\(=\frac{1}{5}-\frac{1}{6}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{5}-\frac{1}{12}\)

\(=\frac{12}{60}-\frac{5}{60}=\frac{7}{60}\)

\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

=\(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{5}-\frac{1}{12}=\frac{7}{60}\)

539/78 k cho mình