A=\(\frac{4}{11}-\frac{4}{13}+\frac{4}{13}-\frac{4}{15}+...+\frac{4}{99}-\frac{4}{101}\)

\(A=4\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(A=4.\left(\frac{1}{11}-\frac{1}{101}\right)\)

A=4. 90/1111=360/1111

Co dung khong vay Cuong Lucha DT

ta lấy : (1/11-1/13+1/13-1/15+...+1/19)x462-y=19

                (1/11-1/19)x462-y=19

                  32/209x462-y=19

                      70,73-y=19

                         y=70,73-19=51,73

đúng thì k cho mình nhé , ko đúng cũng ko sao ^^

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right).462-x=19\)

\(\left(\frac{1}{11}-\frac{1}{13}+...+\frac{1}{19}-\frac{1}{21}\right)\cdot462-x=19\)

\(\left(\frac{1}{11}-\frac{1}{21}\right)\cdot462-x=19\)

\(\frac{10}{231}.462-x=19\)

\(20-x=19\)

\(x=20-19\)

\(x=1\)

Đề abfi sai. Chỗ đó là 19, k phải 29

Bạn biết tính chất này không?

\(\frac{a}{n\left(n+a\right)}=\frac{1}{n}-\frac{1}{n+a}\)

Sử dụng tính chất đó thì được:

\(\left(\frac{2}{11}-\frac{2}{13}+\frac{2}{13}-\frac{2}{15}+...+\frac{2}{19}-\frac{2}{21}\right)\)x 462 - x =19

\(\left(\frac{2}{11}-\frac{2}{21}\right)\cdot462-x=19\)

\(\frac{924}{11}-\frac{924}{21}-x=19\)

84 - 44 - x =19

40 - x = 19

x = 40 - 19

x = 21

Nhớ tk cho mình nếu đúng nhé

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+.....+\frac{2}{19.21}\right).462-x=19\)

\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+......+\frac{1}{19}-\frac{1}{21}\right).462-x=19\)

\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{21}\right).462-x=19\)

\(\Leftrightarrow\frac{10}{231}.462-x=19\)

\(\Leftrightarrow20-x=19\)

\(\Leftrightarrow x=20-19\)

\(\Leftrightarrow x=1\)

2/11x13+2/13x15+2/15x17+...+2/97x99

=1/11-1/13+1/13-1/15+1/15-1/17+...+1/97-1/99

=1/11-1/99

=8/99

thank you 

= 2/11.13 + 2/13.15 + ... + 2/97.99

= 2/11 .2/13 + 2/13 . 2/15 + ... + 2/97 . 2/97

= 2/11 + 2/97

= ......tu tinh

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right)\cdot462-x=19\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)\cdot462-x=19\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{21}\right)\cdot462-x=19\)

\(\Rightarrow\frac{10}{231}\cdot462-x=19\)

\(\Rightarrow20-x=19\Rightarrow x=1\)

Ta có:

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right).462-x=19\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right).462-x=19\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{21}\right).462-x=19\)

\(\Rightarrow\frac{10}{231}.462-x=19\Leftrightarrow20-x=19\)

\(\Rightarrow x=20-19=1\)

Mọi người giúp mik với mik đang cần gấp

\(=\frac{1}{2}\times\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+...+\frac{1}{97}-\frac{1}{99}\right)\)

\(=\frac{1}{2}\times\left(\frac{1}{9}-\frac{1}{99}\right)\)

\(=\frac{1}{2}\times\frac{10}{99}\)

\(=\frac{5}{99}\)

\(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+....+\frac{1}{97}-\frac{1}{99}=\frac{1}{9}_{ }-\frac{1}{99}=\)\(\frac{10}{99}\)

\(A=\frac{1}{11.13}+\frac{1}{13.15}+..+\frac{1}{19.21}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+..+\frac{1}{19}-\frac{1}{21}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{21}\right)\)

\(A=\frac{1}{11\cdot13}+\frac{1}{13\cdot15}+...+\frac{1}{19\cdot21}\)

\(2A=\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+...+\frac{2}{19\cdot21}\)

\(2A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\)

\(2A=\frac{1}{11}-\frac{1}{21}+0+...+0\)

\(2A=\frac{10}{231}\)

\(A=\frac{5}{231}\)