sai đề rồi 

1/2 + 1/6 + 1/12 + ... + 1/132

= 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/11.12

= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/11 - 1/12

= 1 - 1/12

= 11/12

1/90 + 1/110 + 1/132 + ... + 1/10100

= 1/9.10 + 1/10.11 + 1/11.12 + ... + 1/100.101

= ... [như trên]

= 1/9 - 1/100

= 49/450

balabal;a

1/12 + 1/20 + ... + 1/132

= 1/3×4 + 1/4×5 + ... + 1/11×12

= 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/11 - 1/12

= 1/3 - 1/12

= 4/12 - 1/12

= 3/12 = 1/4

\(=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{11.12}\)

\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{3}-\frac{1}{12}\)

\(=\frac{1}{4}\)

1/12 + 1/20 + ... + 1/132

= 1/3.4 + 1/4.5 + 1/6.7 + 1/7.8 + 1/9.10 + 1/10.11 + 1/11.12

= 1/3 - 1/4 + 1/4 - 1/5 + 1/6 - 1/7 + 1/7 - 1/8 + 1/9 - 1/10 + 1/10 - 1/11 + 1/11 - 1/12

= 1/3 - 11/30 - 17/72 - 1/12

= \(-\left(\frac{127}{360}\right)\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+..........+\frac{1}{132}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{11.12}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...........+\frac{1}{11}-\frac{1}{12}\)

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

\(=\frac{11}{12}\)

bài này hóc búa thật

hơi khó 5 chút

1/4

can cach giai ko

Là sao mik chả hỉu gì cả??????

Ta có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

= \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}\)

= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)

= \(1-\frac{1}{12}=\frac{11}{12}\)

1/2 + 6/ 1 + 12/ 1 + ......... + 1/132 = 1/ 1.2  + 1/2.3  + 1/3.4  + .......... +1/ 11.12  = 1 − 1/2  + 1/'2  − 1/3  + 1/3  − 1/4  + ........... + 1/11  − 1/12  = 1 − 1/12  = 11/12

\(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{132}=\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{11\cdot12}\)

\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{3}-\frac{1}{12}=\frac{4}{12}-\frac{1}{12}=\frac{3}{12}=\frac{1}{4}\)

Chú ý: \(\cdot=\times\)

Đặt \(A=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{132}\)

\(A=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{11.12}\)

\(A=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{12}\)

\(\Rightarrow A=\frac{1}{3}-\frac{1}{12}=\frac{1}{4}\)

=1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10+1/10.11+1/11.12

=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12

=1/3-0-0-0-0-0-0-0-0-1/12

=4/12-1/12=3/12=1/4

A = 1 - \(\dfrac{5}{6}\)+\(\dfrac{7}{12}\)-\(\dfrac{9}{20}\)+\(\dfrac{11}{30}\)-\(\dfrac{13}{42}\)+\(\dfrac{15}{56}\) - \(\dfrac{17}{72}\)+\(\dfrac{19}{90}\)+\(\dfrac{23}{132}\)-\(\dfrac{25}{156}\)

A = 1 - \(\dfrac{5}{2.3}\)+\(\dfrac{7}{3.4}\)-\(\dfrac{9}{4.5}\)+\(\dfrac{11}{5.6}\)-\(\dfrac{13}{6.7}\)+\(\dfrac{15}{7.8}\)-\(\dfrac{17}{8.9}\)+\(\dfrac{19}{9.10}\)+\(\dfrac{23}{11.12}\)-\(\dfrac{25}{12.13}\)

A = 1 - \(\dfrac{1}{2}-\dfrac{1}{3}\)+\(\dfrac{1}{3}+\dfrac{1}{4}\)-\(\dfrac{1}{4}-\dfrac{1}{5}\)+...+\(\dfrac{1}{11}+\dfrac{1}{12}\)- \(\dfrac{1}{12}-\dfrac{1}{13}\)

A = 1 - \(\dfrac{1}{2}\) - \(\dfrac{1}{13}\) 

A = \(\dfrac{1}{2}\) - \(\dfrac{1}{13}\)

A = \(\dfrac{11}{26}\) 

1/3-1/12

=1/4

Chúc bạn bạn may mắn!

1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132 = 2/3,

 Đúng 100%!

Ai tk cho mình mình tk lại.