rút gọn chứ ko fai tính à

\(C=\frac{1}{3}.\frac{1}{7}+\frac{1}{7}.\frac{1}{11}+\frac{1}{11}.\frac{1}{13}+...+\frac{1}{2011}.\frac{1}{2015}\)

\(C=\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.13}+...+\frac{1}{2011.2015}\)

\(4C=4\left(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.13}+...+\frac{1}{2011.2015}\right)\)

\(4C=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.13}+...+\frac{4}{2011.2015}\)

\(4C=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+...+\frac{1}{2011}-\frac{1}{2015}\)

\(4C=\frac{1}{3}-\frac{1}{2015}=\frac{2012}{6045}\)

\(C=\frac{2012}{6045}:4=\frac{503}{6045}\)

\(C=\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+....+\dfrac{1}{2011}-\dfrac{1}{2015}\right)\)

\(C=\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{2015}\right)=\dfrac{1}{4}\left(\dfrac{2012}{3.2015}\right)=\dfrac{503}{3.2015}\)

Câu 1.C
Câu 2.B
Câu 3.A
Câu 4.C
Câu 5.C
Câu 6.D
Câu 7.C
Câu 8.D

bài 5

a) 

`7/5xx15/14`

`=105/70=3/2`

b)

`8/15xx25/8`

`=200/120=5/3`

c)

`2/15xx5/22`

`=10/330`

`=1/33`

bài 6

chiều rộng cx là đơn vị m phải ko ạ?

diện tích căn phòng là

`11/2xx7/2=77/4(m^2)`

\(\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}+\frac{1}{6}.\frac{1}{7}+\frac{1}{7}.\frac{1}{8}+\frac{1}{8}.\frac{1}{9}\)

\(=\frac{1.1}{2.3}+\frac{1.1}{3.4}+\frac{1.1}{4.5}+\frac{1.1}{5.6}+\frac{1.1}{6.7}+\frac{1.1}{7.8}+\frac{1.1}{8.9}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)

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

\(=\frac{7}{18}\)

= 1/2.3+1/3.4+1/4.5+...+1/8.9

= 1/2-1/3+1/3-1/4+...+1/8-1/9

= 1/2-1/9

= 7/18