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

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

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

\(=\dfrac{1}{1}\cdot\dfrac{1}{2}+\dfrac{1}{2}\cdot\dfrac{1}{3}+\dfrac{1}{3}\cdot\dfrac{1}{4}+\dfrac{1}{4}\cdot\dfrac{1}{5}+\dfrac{1}{5}\cdot\dfrac{1}{6}+\dfrac{1}{6}\cdot\dfrac{1}{7}\)

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

\(=\dfrac{1}{1}-\dfrac{1}{7}=\dfrac{7}{7}-\dfrac{1}{7}=\dfrac{6}{7}\)

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

= \(-\left(\frac{127}{360}\right)\)

1/4

can cach giai ko

=1/1*2+1/2*3+1/3*4+...+1*10*11+1/11*12=1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11+1/11-1/12

=1-1/12=11/12.

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}+\frac{1}{132}\)

\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{10\times11}+\frac{1}{11\times12}\)

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

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

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

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}+\frac{1}{132}\)

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

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

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

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

k mình nha ! Chúc bạn học giỏi ! ^_^