Gọi tổng bằng S

1/9 S=1/15*18+..................+1/87*90

1/9 S=1/15-1/18+1/18-......................-1/90

1/9 S=1/15-1/90

1/9 S=1/18

S=9/18=1/2

bạn sai ở đoạn cuối

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

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!!!

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

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

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

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

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

Đặt \(A=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)

\(A=2.\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\right)\)

\(A=2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(A=2.\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(A=2.\frac{1}{18}=\frac{1}{9}\)

Vậy...

\(A=2.\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\right)\)

\(A=2.\left(\frac{1}{15}-\frac{1}{18}+.......+\frac{1}{87}-\frac{1}{90}\right)\)

\(A=2.\left(\frac{1}{15}-\frac{1}{90}\right)\)

-Các ước của 42 là 1;2;3;6;7;21

 Tổng các ước của 42 là: 

        1+2+3+6+7+21=36

- Các bội của 6 lớn hơn 100 và bé hơn 200 là: (tìm ra rồi công lại giống o trên