=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 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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!

=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

Ta có : 

\(G=\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{97.99}+\frac{2}{99.101}\)

\(G=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\)

\(G=\left(\frac{1}{13}-\frac{1}{13}\right)+\left(\frac{1}{15}-\frac{1}{15}\right)+\left(\frac{1}{17}-\frac{1}{17}\right)+...+\left(\frac{1}{99}-\frac{1}{99}\right)+\left(\frac{1}{11}-\frac{1}{101}\right)\)

\(G=\frac{1}{11}-\frac{1}{101}\)

\(G=\frac{101}{1111}-\frac{11}{1111}\)

\(G=\frac{101-11}{1111}\)

\(G=\frac{90}{1111}\)

Vậy \(G=\frac{90}{1111}\)

Chúc bạn học tốt ~

\(G=\frac{2}{11\times13}+\frac{2}{13\times15}+\frac{2}{15\times17}+...+\frac{2}{97\times99}+\frac{2}{99\times101}\)

\(G=2\times\left(\frac{1}{11\times13}+\frac{1}{13\times15}+\frac{1}{15\times17}+...+\frac{1}{97\times99}+\frac{1}{99\times101}\right)\)

\(G=2\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\right)\)

( GẠCH BỎ CÁC PHÂN SỐ GIỐNG NHAU TRONG NGOẶC)

\(G=2\times\left(\frac{1}{11}-\frac{1}{101}\right)\)

\(G=2\times\frac{90}{1111}\)

\(G=\frac{180}{1111}\)

MK VIẾT ĐỀ BÀI NHƯ THẾ CÓ ĐÚNG KO BN!

MK CHỈ NGHĨ RA VẬY THÔI

CHÚC BN HỌC TỐT!!!!

\(\frac{3}{11\text{x}13}+\frac{3}{13\text{x}15}+\frac{3}{15\text{x}17}+\frac{3}{17\text{x}19}+\frac{3}{19\text{x}21}\)

\(=\frac{3}{2}\text{x}\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right)\)

\(=\frac{3}{2}\text{x}\left(\frac{1}{11}-\frac{1}{21}\right)\)

\(=\frac{3}{2}\text{x}\frac{10}{231}\)

\(=\frac{5}{77}\)

\(A=13.15+15.17+17.19+...+99.101\)

\(\Rightarrow6A=13.15.6+15.17.6+17.19.6+...+99.101.6\)

\(\Rightarrow6A=13.15.\left(17-11\right)+15.17.\left(19-13\right)+17.19.\left(21-15\right)+...+99.101.\left(103-97\right)\)

\(\Rightarrow6A=\left(13.15.17-11.13.15\right)+\left(15.17.19-13.15.17\right)+\left(17.19.21-15.17.19\right)+...+\left(99.101.103-97.99.101\right)\)

\(\Rightarrow6A=99.101.103-11.13.15\)

\(\Rightarrow6A=1027752\)

\(\Rightarrow A=171292\)

Câu1:                     750

Câu2:                     \(\approx\)5240,322

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