=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6

=1/2-1/6=1/3

\(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}=\dfrac{1}{2}-\dfrac{1}{6}=\dfrac{3-1}{6}=\dfrac{2}{6}=\dfrac{1}{3}\)

1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6

=1/2-1/6

=3/6-1/6

=2/6=1/3

=1/2-1/3+1/3-1/4+...+1/6-1/7

=1/2-1/7

=5/14

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)

\(=\dfrac{1}{2}-\dfrac{1}{6}\)

\(=\dfrac{1}{3}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}=\dfrac{1}{2}-\dfrac{1}{6}=\dfrac{1}{3}\)

1/1x2+1/2x3+1/3x4+..+1/9x10

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5+...-1/10

=1-1/10

=9/10

\(\dfrac{87x52x64}{58x26x16}=\dfrac{29x3x2x4}{58}=\dfrac{3x4}{1}=12\)

*Thực hiện phương pháp gạch bỏ*

1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7

=1/1-1/2+1/2-1/3+...-1/7

=1+(1/2-1/2+1/3-1/3+...+1/6-1/6)-1/7

=1 +0+0+...-1/7

=1-1/7

=6/7

hình như là 8/7
 

Kếết quả là 116/24

Rút gọn ra phân số tối giản là 29/6

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)

Đặt \(M=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(M=1-\frac{1}{100}\)

\(M=\frac{99}{100}\)

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+....+\frac{1}{99\times100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)