\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)

( GẠCH BỎ CÁC PHÂN SỐ GIỐNG NHAU)

\(=\frac{1}{2}-\frac{1}{10}\)

\(=\frac{5}{10}-\frac{1}{10}\)

\(=\frac{4}{10}=\frac{2}{5}\)

CHÚC BẠN HỌC TỐT!!!!!!!!

\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+.....+\frac{1}{9\times10}\)

Đặt \(A=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+.....+\frac{1}{9\times10}\)

Nhận xét:

\(\frac{1}{2\times3}=\frac{1}{2}-\frac{1}{3};\frac{1}{3\times4}=\frac{1}{3}-\frac{1}{4}\)

\(\frac{1}{4\times5}=\frac{1}{4}-\frac{1}{5};......;\frac{1}{9\times10}=\frac{1}{9}-\frac{1}{10}\)

Do đó \(A=\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(A=\frac{1}{2}-\frac{1}{10}\)

\(A=\frac{2}{5}\)

= 1/9 + 1/6 = 5/18

~~~hok tốt~~~

1/9+8/9.3/16

=1/9+1/6

=5/18

khó thấy quá bạn ơi

A=(3/10+4/5x1/2):(1/8/9-1/1/3)

A=(3/10+2/5):5/9

A=7/10:5/9

A=63/50

=( 19/13+7/13) + ( 17/9+1/9) + ( 7/3 + 2/3)

= 26/13 + 18/9 + 9/3

= 2 + 2+3

= 7

4-\(\frac{4}{9}\)- [\(2\frac{1}{4}\)+1\(\frac{4}{9}\)]

=\(4-\frac{4}{9}-2\frac{1}{4}-1\frac{4}{9}\)

=\(\left(4-2\frac{1}{4}\right)-\left(\frac{4}{9}-1\frac{4}{9}\right)\)

=\(1\frac{3}{4}-\left(-1\right)\)

=\(2\frac{3}{4}\)