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

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!!!

a) đặt  \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\)

\(\Rightarrow2\times A=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{128}\)

\(\Rightarrow2\times A-A=1-\frac{1}{256}\)

\(A=\frac{255}{256}\)

phần b bn cx lm tương tự như z nha!

c) sửa đề:

\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{13x14}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{13}-\frac{1}{14}\)

\(=1-\frac{1}{14}=\frac{13}{14}\)

Sửa:

d) \(\frac{1}{15x18}+\frac{1}{18x21}+\frac{1}{21x24}+...+\frac{1}{87x90}\)

\(=\frac{1}{3}x\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(=\frac{1}{3}x\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(=\frac{1}{3}x\frac{1}{18}\)

\(=\frac{1}{54}\)

bạn sai ở đoạn cuối

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

D=6/15.18+6/18.21+...+6/89.92

D=6(1/15.18+1/18.21+...+1/89.92)

a) 3D=6(1/15-1/18+1/18-1/21+...+1/89-1/92)

3D=6(1/15-1/92)

3D=6.(77/1380)

3D=77/230

D=77/690

b) F=1/25.27+1/27.29+...+1/73.75

2F=2/25.27+2/27.29+..+2/73.75

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

2F=1/25-1/75

2F=2/75

F=1/75

A.3=5.3/18.21+5.3/21.24+5.3/24.27+...+5.3/123.126

A.3=5/18-5/21 +  5/21-5/24 + 5/24-5/27 +...+ 5/123-5/126

A.3=5/18-5/126

A.3=   5/21

A  =5/21:3

A  =  5/63

    Đây là cách của mik nếu sai thì thôi nhé

Kết quả đúng rồi đấy !

A=5/3 x (3/(18x21) + 3/(21x24) + 3/(24x27) + ... + 3/(123x 126)

A=5/3 x (1/18 - 1/21 + 1/21 - 1/24 + 1/24 - 1/27 +...+1/ 123 - 1/ 126)

A=5/3x(1/8-1/126)

A=5/3x 1/21

A=5/63