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

\(\dfrac{4}{9\cdot11}+\dfrac{4}{11\cdot13}+...+\dfrac{4}{97\cdot99}\)

\(=2\left(\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}+...+\dfrac{2}{97\cdot99}\right)\)

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

\(=2\cdot\left(\dfrac{1}{9}-\dfrac{1}{99}\right)\)

\(=2\cdot\dfrac{10}{99}=\dfrac{20}{99}\)

=2/11+2/13-2/13+2/15-2/15+...-2/97+2/98

=2/11+(2/13-2/13+2/15-2/15+...-2/97+2/99)

=2/11+2/99

=20/99

\(\frac{2}{11}\times13+\frac{2}{13}\times15+\frac{2}{15}\times17+........+\frac{2}{97}\times99\)

\(A\times2=\frac{2}{11\times13}+\frac{2}{13\times15}+\frac{2}{15\times17}+........+\frac{2}{97\times99}\)

\(A\times2=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+........+\frac{1}{97}-\frac{1}{99}\)

\(A=\frac{1}{11}-\frac{1}{99}\)

\(A=\frac{8}{99}\)

mik ko bt là có đúng hay ko nhưng đúng thì các bạn cho 1 t i c k nha

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

Mọi người giúp mik với mik đang cần gấp

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

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

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

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

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

\(\frac{4}{9\times11}+\frac{4}{11\times13}+\frac{4}{13\times15}+...+\frac{4}{95\times97}+\frac{4}{97\times99}\)

\(=2\times\left(\frac{2}{9\times11}+\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{95\times97}+\frac{2}{97\times99}\right)\)

\(=2\times\left(\frac{11-9}{9\times11}+\frac{13-11}{11\times13}+\frac{15-13}{13\times15}+...+\frac{97-95}{95\times97}+\frac{99-97}{97\times99}\right)\)

\(=2\times\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{97}+\frac{1}{97}-\frac{1}{99}\right)\)

\(=2\times\left(\frac{1}{9}-\frac{1}{99}\right)=\frac{20}{99}\)

4/9x11 + 4/11x13 + 4/13X15 + .............+ 4/95X97 + 4/97X99

=2 x (2/9x11 + 2/11x 13 + .........+2/95x97 + 2/97x99)

=2 x ( 1/9 - 1/11 + 1/11- 1/13 +...... + 1/97 - 1/99)

=2 x (1/9 - 1/99)

=2 x10/99

=20/99

Học tốt!

\(\frac{2}{11x13}+\frac{2}{13x15}+\frac{2}{15x17}+...+\frac{2}{97x99}\)

\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}\)

\(=\frac{1}{11}-\frac{1}{99}\)

\(=\frac{8}{99}\)

=1/11 - 1/13 + 1/13 - 1/15 +...+1/19 - 1/21

=1/11-1/21=10/231