Gọi A = 2/11.13 +2/13.15+2/15.17 +...+2/53.55

=> A = 1/11-1/13+1/13-1/15+...+1/53-1/55

=> A = 1/11-1/55

=> A = 4/55

Đúng 100%

=1/11-1/13+1/13-1/15+1/15-1/17+...+1/53-1/55

=1/11-1/55

=5/55-1/55

=4/55

\(\frac{2}{11.13}+\frac{2}{13.15}+.....+\frac{2}{209.211}\)

\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)\(+.....+\frac{1}{209}-\frac{1}{211}\)

\(=\frac{1}{11}-\frac{1}{211}=\frac{200}{2321}\)

hok tốt

Đặt \(A=\text{2 : [ 11.13 ] + 2 : [ 13.15 ] + 2 : [ 15.17 ] + ...+ 2 : [ 209.211]}\)

\(\Rightarrow A=\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}...+\frac{2}{209.211}\)

\(\Rightarrow A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{209}-\frac{1}{211}\)

\(\Rightarrow A=\frac{1}{11}-\frac{1}{211}\)

\(\Rightarrow A=\frac{200}{2321}\)

~Study well~

Sai thì thôi nhé :D !

\(2:\left(11.13\right)+2:\left(13.15\right)+2:\left(15.17\right)+...+2:\left(209:211\right)\)

\(=\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{209.211}\)

\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{209}-\frac{1}{211}\)

\(=\frac{1}{11}+\left(\frac{1}{13}-\frac{1}{13}\right)+\left(\frac{1}{15}-\frac{1}{15}\right)+...+\left(\frac{1}{209}-\frac{1}{209}\right)-\frac{1}{211}\)

\(=\frac{1}{11}-\frac{1}{211}=\frac{200}{2321}\)

~ Hok tốt ~

http://olm.vn/hoi-dap/question/136755.html

bạn vào đây sẽ thấy bài giải mik vừa giải xong đó

cho mik đúng nha

\(C=\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{2015.2017}\)

\(2C=\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{2015.2017}\)

\(2C=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{2015}-\frac{1}{2017}\)

\(2C=\frac{1}{11}-\frac{1}{2017}\)

\(2C=\frac{2006}{22187}\)

\(C=\frac{1003}{22187}\)

C = 1/11 . 13 + 1/13 . 15 + 1/15 . 17 + ........ + 1/2015 . 2017

C = 1/11 - 1/13 + 1/13 - 1/15 + 1/15 - 1/17 + ......... + 1/2015 - 1/2017

C = 1/11 - 1/2017

C = 2006/22187

\(C=\frac{1}{11\cdot13}+\frac{1}{13\cdot15}+\frac{1}{15\cdot17}+...+\frac{1}{2015\cdot2017}\)

\(C=\frac{1}{2}\cdot\left(\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+\frac{2}{15\cdot17}+...+\frac{2}{2015\cdot2017}\right)\)

\(C=\frac{1}{2}\cdot\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17} +...+\frac{1}{2015}-\frac{1}{2017}\right)\)

\(C=\frac{1}{2}\cdot\left(\frac{1}{11}-\frac{1}{2017}\right)\)

\(C=\frac{1}{2}\cdot\frac{2006}{22187}=\frac{1003}{22187}\)

Đặt \(A=\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}^{ }\)

\(A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\)

\(A=\frac{1}{11}-\frac{1}{21}\)

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

Thay \(A=\frac{10}{231}\) vào ta có

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

\(20-x=19\)

\(x=20-19\)

\(x=1\)

boi vi\(\frac{10}{231}.462=20\) cho mik dung nha

=(1/11-1/13)+(1/13-1/15)+(1/15-1/17)+(1/17-1/19)+(1/19-1/21)*462-X=19

=(1/11-1/21)*462-X=19

=10/231*462-X=19

=20-X=19

=X=20-19

=X=1

lop nam cung lam duoc

Đề là tìm x hả bạn!!

\(x-\dfrac{20}{11.13}-\dfrac{20}{23.15}-....-\dfrac{20}{53.55}=\dfrac{3}{11}\)

\(x-\left(\dfrac{20}{11.13}+\dfrac{20}{13.15}+....+\dfrac{20}{53.55}\right)=\dfrac{3}{11}\)

\(x-10\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}+...+\dfrac{1}{53}-\dfrac{1}{55}\right)=\dfrac{3}{11}\)

\(x-10\left(\dfrac{1}{11}-\dfrac{1}{55}\right)=\dfrac{3}{11}\)

\(x-\dfrac{8}{11}=\dfrac{3}{11}\)

=> \(x=\dfrac{3}{11}+\dfrac{8}{11}=1\)

Ta có:

x-\(\frac{20}{11.13}\)-\(\frac{20}{13.15}\)-\(\frac{20}{15.17}\)-...-\(\frac{20}{53.57}\)=\(\frac{3}{11}\)

\(\Rightarrow\)\(\frac{20}{11.13}\)-\(\frac{20}{13.15}\)-\(\frac{20}{15.17}\)-...-\(\frac{20}{53.57}\)= x-\(\frac{3}{11}\)

\(\frac{1}{10}\).\((\frac{20}{11.13}.\frac{20}{13.15}.\frac{20}{15.17}...\frac{20}{53.57})\)= x-\(\frac{3}{11}\)

\(\frac{2}{11.13}\).\(\frac{2}{13.15}\).\(\frac{2}{15.17}\)...\(\frac{2}{53.57}\)= x-\(\frac{3}{11}\)

\(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}\)-\(\frac{1}{17}\)+...+\(\frac{1}{53}\)-\(\frac{1}{57}\)=x-\(\frac{3}{11}\)

\(\frac{1}{11}-\frac{1}{57}\)=x-\(\frac{3}{11}\)

\(\frac{46}{627}\)=x-\(\frac{3}{11}\)

x=\(\frac{46}{627}\)-\(\frac{3}{11}\)

Vậy x=\(\frac{-125}{627}\)