a) A = 9/8.11 + 9/11.14 + 9/14.17 + ... + 9/73.75

A = 3.(1/8 - 1/11 + 1/11 - 1/14 + 1/14 - 1/17 + ... + 1/73 - 1/75)

A = 3.(1/8 - 1/75)

A = 3.67/600

A = 67/200

Các bài sau làm tương tự, riêng câu D thì phân tích ra 

Mình chỉ làm hộ bạn câu a) thôi nhé vì đề sàn sàn giống nhau :

a) \(A=\frac{9}{8×11}+\frac{9}{11×14}+\frac{9}{14×17}+...+\frac{9}{73×75}\)

\(A=\frac{9}{8}-\frac{9}{11}+\frac{9}{11}-\frac{9}{14}+\frac{9}{14}-\frac{9}{17}+...+\frac{9}{73}-\frac{9}{75}\)

\(A=\frac{9}{8}-\frac{9}{75}\)

\(A=\frac{675}{600}-\frac{72}{600}\)

\(A=\frac{673}{600}\)

Vậy,...

Cbht

\(d,D=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

\(10D=\frac{1}{7\cdot8}+\frac{1}{2\cdot70}+\frac{1}{2\cdot130}+...+\frac{1}{2\cdot700}\)

\(10D=\frac{1}{7}-\frac{1}{8}+\frac{1}{2}-\frac{1}{70}+\frac{1}{2}-\frac{1}{130}+...+\frac{1}{2}-\frac{1}{700}\)

\(10D=\frac{1}{7}-\frac{1}{700}\)

\(10D=\frac{99}{700}\)

\(D=\frac{99}{700}:10\)

\(D=\frac{99}{7000}\)

gợi ý nè

1/a.b=1/a-1/b

b. B= 1/25×27+1/27×29+1/29×31+...+1/73×75

2B= 2.(1/25×27+1/27×29+1/29×31+...+1/73×75)

2B= 2/25×27+2/27×29+2/29×31+...+2/73×75

2B= 1/25-1/27+1/27-1/29+...+1/73-1/75

2B= 1/25-1/75

B=(1/25-1/75):2

Từng đó đã nha để mik nghĩ tiếp

T.i.c.k đc ko PLEASE!!!

\(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)

\(B=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)

\(B=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\)

\(B=\frac{1}{2}\cdot\frac{2}{75}\)

\(B=\frac{1}{75}\)

\(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+....+\frac{1}{73.75}\)

\(B=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)

\(B=\frac{1}{2}\cdot\left(\frac{1}{25}-\frac{1}{75}\right)\)

\(B=\frac{1}{2}\cdot\frac{2}{75}=\frac{1}{75}\)

Theo đề bài ta có:

\(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)

\(\Leftrightarrow B=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)

\(\Leftrightarrow B=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}\right)\)

\(\Leftrightarrow B=\frac{1}{2}\cdot\frac{2}{75}\)

\(\Leftrightarrow B=\frac{1}{75}\)

tôi cũng hỏi bạn

bạn sai ở đoạn cuối

A=\(\frac{3\cdot3}{15\cdot18}+\frac{3\cdot3}{18\cdot21}+...+\frac{3\cdot3}{96\cdot99}=3\cdot\left(\frac{3}{15\cdot18}+\frac{3}{18\cdot21}+...+\frac{3}{96\cdot99}\right)=3\cdot\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{96}-\frac{1}{99}\right)=3\cdot\left(\frac{1}{15}-\frac{1}{99}\right)=3\cdot\frac{28}{495}=\frac{28}{165}\)

\(\left(\frac{1}{25x27}+\frac{1}{27x29}+\frac{1}{29x31}+....+\frac{1}{73x75}\right)x\frac{3}{10}=x\)

\(< =>\frac{1}{2}x\left(\frac{2}{25x27}+\frac{2}{27x29}+\frac{2}{29x31}+....+\frac{2}{73x75}\right)x\frac{3}{10}=x\)

\(< =>\frac{1}{2}x\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+....+\frac{1}{73}-\frac{1}{75}\right)x\frac{3}{10}=x\)

\(< =>\frac{1}{2}x\left(\frac{1}{25}-\frac{1}{75}\right)x\frac{3}{10}=x< =>\frac{1}{2}x\frac{2}{25}x\frac{3}{10}=x< =>x=\frac{3}{250}\)

 B8 = 6/15.18 + 6/18.21 + 6/21.24 + ... + 6/87.90

 B8 = 2.(3/15.18 + 3/18.21 + 3/21.24 + ... + 3/87 .90)

 B8 = 2.(1/15 - 1/18 + 1/18 -1/21 + 1/21 - 1/24 + ... + 1/87 - 1/90)

 B8 = 2.(1/15 - 1/90)

 B8 = 2.(6/90 - 1/90)

 B8 = 2. 1/18

 B8 = 1/9

 B = 1/9 : 8

 B = 1/72

thank bạn nha