Question

[Nguyễn Thị Phương Thảo]

Tính giá trị biểu thức sau theo cách hợp lí

A = 9 / 15 x 18 + 9 /18 x 21 + 9 / 21 x 24 +......+ 9 / 89 x 90

Answer 1

[Sherlockichi Kazukosho]

\(A=\frac{9}{15.18}+\frac{9}{18.21}+.....+\frac{9}{89.92}\)

\(A=3.\left(\frac{3}{15.18}+\frac{3}{18.21}+....+\frac{3}{89.92}\right)\)

\(A=3.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+......+\frac{1}{89}-\frac{1}{92}\right)\)

\(A=3.\left(\frac{1}{15}-\frac{1}{92}\right)\)

\(A=3.\frac{77}{1380}=\frac{77}{460}\)

Answer 2

[Phan Bình Bảo Lâm]

$A=\frac{9}{15.18}+\frac{9}{18.21}+.....+\frac{9}{89.92}$

$A=3.\left(\frac{3}{15.18}+\frac{3}{18.21}+....+\frac{3}{89.92}\right)$

$A=3.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+......+\frac{1}{89}-\frac{1}{92}\right)$

$A=3.\left(\frac{1}{15}-\frac{1}{92}\right)$

$A=3.\frac{77}{1380}=\frac{77}{460}$