Question

1/15×18+1/18×21+1/21×24+...+1/87×90

Answer 1

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

Answer 2

   Đặt tổng trên là A

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

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

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

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

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

                                 \(#Louis\)