= 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/7-1/8+1/8-1/9
=1/2-1/9
= 7/18

\(S=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2004.2005}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2004}-\dfrac{1}{2005}\\ =1-\dfrac{1}{2005}\\ =\dfrac{2004}{2005}\)

= 1/2-1/3+1/3-1/4+1/4-1/5+.........+ 1/19-1/20

= 1/2-1/20

= 9/20

ok bn

=25 năm 

Tui lộn 9/20 nha

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

=1-1/6

=5/6

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

=1-1/6

=5/6

\(\frac{1}{1x2}+\frac{1}{1x3}+...+\frac{1}{999x1000}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{999}-\frac{1}{1000}\)

\(=1-\frac{1}{1000}\)

\(=\frac{999}{1000}\)

1/1x2+1/2x3+1/3x4+...+1/999x1000

=1-1/2+1/2-1/3+1/3-1/4+...+1/999-1/1000

=1-1/1000

=1000/1000-1/1000

=999/1000

999 / 1000

A = 1/1x2 + 1/2x3 + 1/3x4 + .......... + 1/9x19

A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .......... + 1/18 - 1/19

A = 1 - 1/19

A = 18 /19

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{14.15}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{14}-\frac{1}{15}\)

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

\(A=\frac{14}{ }15\)

=1-1/2+1/2-1/3+...+1/14-1/15

=1-1/15

=14/15

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{14.15}=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+...+\left(\frac{1}{14}-\frac{1}{15}\right).\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}=1-\left(\frac{1}{2}-\frac{1}{2}\right)_{ }-...-\left(\frac{1}{14}-\frac{1}{14}\right)-\frac{1}{15}_{ }.\)

\(=1-\frac{1}{15}=\frac{14}{15}.\)

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

\(5\dfrac{9}{10}:\dfrac{3}{2}-\left(2\dfrac{1}{3}\times4\dfrac{1}{2}-2\times2\dfrac{1}{3}\right):\dfrac{7}{4}\)

\(=\dfrac{59}{10}:\dfrac{3}{2}-\left(\dfrac{7}{3}\times\dfrac{9}{2}-2\times\dfrac{7}{3}\right):\dfrac{7}{4}\)

\(=\dfrac{59}{10}\cdot\dfrac{2}{3}-\left[\dfrac{7}{3}\times\left(\dfrac{9}{2}-2\right)\right]:\dfrac{7}{4}\)

\(=\dfrac{59}{15}-\left(\dfrac{7}{3}\times\dfrac{5}{2}\right):\dfrac{7}{4}\)

\(=\dfrac{59}{15}-\dfrac{35}{6}\cdot\dfrac{4}{7}\)

\(=\dfrac{59}{15}-\dfrac{10}{3}\)

\(=\dfrac{59}{15}-\dfrac{50}{15}\)

\(=\dfrac{9}{15}\)

\(=\dfrac{3}{5}\)

\(Toru\)

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