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

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

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

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

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

2/11x13+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

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

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

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

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

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

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

=4x(\(\frac{1}{11x13}\)+\(\frac{1}{13x15}\)+.......+\(\frac{1}{99x101}\))

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

4x(\(\frac{1}{11}\)-\(\frac{1}{101}\))

=4x \(\frac{90}{1111}\)

=\(\frac{360}{1111}\)

\(\frac{4}{11\times13}+\frac{4}{13\times15}+\frac{4}{15\times17}+...+\frac{4}{99\times101}\)

\(=\frac{4}{11}-\frac{4}{13}+\frac{4}{13}-\frac{4}{15}+\frac{4}{15}-\frac{4}{17}+...+\frac{4}{99}-\frac{4}{101}\)

\(=\frac{4}{11}-\frac{4}{101}\)

\(=\frac{360}{1111}\)

Đặt biểu thức là A . Ta co 

\(A=\frac{4}{11.13}+\frac{4}{13.15}+....+\frac{4}{99.101}\)

\(\Rightarrow2\left(\frac{2}{11.13}+\frac{2}{13.15}+....+\frac{2}{99.101}\right)\)

\(\Rightarrow A=2\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+.....+\frac{1}{99}-\frac{1}{101}\right)\)

\(\Rightarrow A=2\left(\frac{1}{11}-\frac{1}{101}\right)\)

\(\Rightarrow A=\frac{2.90}{1111}=\frac{180}{1111}\)

2/(7 × 9) + 2/(9 × 11) + 2/(11 × 13) + ... + 2/(97 × 99)

= 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + ... + 1/97 - 1/99

= 1/7 - 1/99

= 92/693

\(B=\frac{4}{1\times3}+\frac{4}{3\times5}+...+\frac{4}{9\times11}+\frac{4}{11\times13}\)

   \(=2\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+...+\frac{2}{9\times11}+\frac{2}{11\times13}\right)\)

   \(=2\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

   \(=2\times\left(1-\frac{1}{13}\right)\)

   \(=2\times\frac{12}{13}\)

   \(=\frac{24}{13}\)

B = \(\frac{4}{1.3}+\frac{4}{3.5}+...+\frac{4}{11.13}\)

\(=4\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{11.13}\right)\)

\(=4.\frac{1}{4}.\left(\frac{2}{1}-\frac{2}{3}+\frac{2}{3}-\frac{2}{5}+...+\frac{2}{11}-\frac{2}{13}\right)\)

\(=2-\frac{2}{13}=\frac{24}{13}\)

\(B=\)\(\frac{4}{1.3}\)\(+\)\(\frac{4}{3.5}\)\(+...+\)\(\frac{4}{9.11}\)\(+\)\(\frac{4}{11.13}\)

\(B=\)\(\frac{4}{2}.\)\(\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{9.11}+\frac{2}{11.13}\right)\)

\(B=\)\(2.\)\(\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(B=\)\(2.\)\(\left(1-\frac{1}{13}\right)\)\(=\)\(2.\frac{12}{13}\)\(=\)\(\frac{24}{13}\)

#Dấu "." là dấu nhân.

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