\(D=\frac{6}{15\times18}+\frac{6}{18\times21}+\frac{6}{21\times24}+...+\frac{6}{87\times90}\)

\(=2\times\left(\frac{3}{15\times18}+\frac{3}{18\times21}+...+\frac{3}{87\times90}\right)\)

\(=2\times\left(\frac{18-15}{15\times18}+\frac{21-18}{18\times21}+...+\frac{90-87}{87\times90}\right)\)

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

\(=2\times\left(\frac{1}{15}-\frac{1}{90}\right)=\frac{1}{9}\)

1/15.18 + 1/18.21 + 1/21.24 + ... + 1/87.90

= 1/3.(3/15.18 + 3/18.21 + 3/21.24 + ... + 3/87.90)

= 1/3.(1/15 - 1/18  + 1/18 - 1/21 + 1/21 - 1/24 + ... + 1/97 - 1/90)

= 1/3.(1/15 - 1/90)

= 1/3.1/18

= 1/54

   Đặt tổng trên là A

3A = \(\frac{1\cdot3}{15\cdot18}+\frac{1\cdot3}{18\cdot21}+...+\frac{1\cdot3}{87\cdot90}\)

\(=\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\)

\(=\frac{1}{15}-\frac{1}{90}\)

\(=\frac{1}{30}\)

\(A=\frac{1}{30}\div3=\frac{1}{30\cdot3}=\frac{1}{90}\)

                                 \(#Louis\)

\(s=\frac{6}{15\times18}+\frac{6}{18\times21}+\frac{6}{21\times24}+....+\frac{6}{87\times90}\)

\(s-3=\frac{3}{15\times18}+\frac{3}{18\times21}+\frac{3}{21\times24}+....+\frac{3}{87\times90}\)

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

\(s-3=\frac{1}{15}-\frac{1}{90}\)

\(s-3=\frac{1}{18}\)

\(s=\frac{1}{18}+3\)

\(s=\frac{55}{18}\)

-1306, 66

12 . 25 + (-134) . 12 + (-12) : (-9)

=  12. [25+(-134) +9]

= 12. (-100)

=-1200

`12 1/4 \div 4/3 + 4 1/4 \div (-4/3)`

`= 12 1/4 * 3/4 + 4 1/4 * (-3/4)`

`= 3/4 * (12 1/4 - 4 1/4)`

`= 3/4 * 8`

`= 24/4 = 6`

\(=\dfrac{49}{4}\cdot\dfrac{3}{4}+\dfrac{17}{4}\cdot\dfrac{-3}{4}\)

=3/4(49/4-17/4)

=3/4*8=6

a)  -374

b)  -1800

\(A=\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{107.111}\)

\(A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{107}-\frac{1}{111}\)

\(A=\frac{1}{3}-\frac{1}{111}\)

\(A=\frac{12}{37}\)

mà dài quá bạn ơi ban tách ra thành nhiều câu hỏi đi thế này trả lời lâu lắm