a: \(=\dfrac{1}{50}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)

\(=\dfrac{1}{5}-\dfrac{49}{50}=\dfrac{-48}{50}=-\dfrac{24}{25}\)

501​−(1−21​+21​−31​+...+491​−501​)

=15−4950=−4850=−2425=51​−5049​=50−48​=−2524​
 

`1/2 -1/6- 1/9`

`= 3/6 -1/6 -1/9`

`= 2/6 -1/9`

`= 1/3-1/9`

`=3/9-1/9`

`=2/9`

\(\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{1}{9}=\dfrac{9}{18}-\dfrac{3}{18}-\dfrac{2}{18}=\dfrac{4}{18}=\dfrac{2}{9}\)

1/2 - 1/6 - 1/9 = 9/18 - 3/18 - 2/18= 4/18

Rút gọn còn 2/9

1) \(\sqrt{1\dfrac{9}{16}}=\sqrt{\dfrac{25}{16}}=\dfrac{5}{4}\)

2) \(\dfrac{\sqrt{12.5}}{0.5}=\sqrt{\dfrac{12.5}{0.25}}=5\sqrt{2}\)

3) \(\sqrt{\dfrac{25}{64}}=\dfrac{5}{8}\)

4) \(\dfrac{\sqrt{230}}{\sqrt{2.3}}=\sqrt{\dfrac{230}{2.3}}=\sqrt{100}=10\)

5) \(\left(\sqrt{\dfrac{2}{3}}+\sqrt{\dfrac{50}{3}}-\sqrt{24}\right)\cdot\sqrt{6}\)

\(=\left(\dfrac{\sqrt{2}}{\sqrt{3}}+\dfrac{5\sqrt{2}}{\sqrt{3}}-2\sqrt{6}\right)\cdot\sqrt{6}\)

\(=\left(\dfrac{6\sqrt{2}}{\sqrt{3}}-2\sqrt{6}\right)\cdot\sqrt{6}\)

\(=0\cdot\sqrt{6}=0\)

`1/( 1.2 ) + 1/( 2.3 ) + .......+1/(99.100)`

`= 1-1/2+1/2-1/3+.....+1/99-1/100`

`=1-1/100`

`=99/100`

=1-1/2+1/2-1/3+...+1/99-1/100

=1-1/100=99/100

\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+....+\dfrac{1}{99.100}\)

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

\(=1-\dfrac{1}{100}=\dfrac{99}{100}\)

Giúp mình

Ta có: \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{2004.2005.2006}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{2004.2005}-\frac{1}{2005.2006}\)

\(=\frac{1}{1.2}-\frac{1}{2005.2006}\)

\(=\frac{1}{2}-\frac{1}{4022030}\)

\(=-40220295.\)

\(=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{2}-\frac{1}{3}-\frac{1}{4}+...-\frac{1}{2005}+\frac{1}{2004}-\frac{1}{2005}-\frac{1}{2006}\)

\(=1-\frac{1}{2006}=\frac{2005}{2006}\)

\(1,=\dfrac{1}{12}-\dfrac{4}{12}=\dfrac{3}{12}\\ 2,=\dfrac{6}{36}-\dfrac{1}{36}=\dfrac{5}{36}\\ 3,\dfrac{-1}{6}-\dfrac{2}{5}=\dfrac{-5}{30}-\dfrac{12}{30}=\dfrac{-17}{30}\\ 4,=\dfrac{15}{20}-\dfrac{1}{20}=\dfrac{14}{20}\)

1,=112−412=3122,=636−136=5363,−16−25=−530−1230=−17304,=1520−120=1420

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

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

\(\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{4}{12}-\dfrac{3}{12}=\dfrac{1}{12}\)

\(\dfrac{1}{4}-\dfrac{1}{5}=\dfrac{5}{20}-\dfrac{4}{20}=\dfrac{1}{20}\)

\(\dfrac{1}{5}-\dfrac{1}{6}=\dfrac{6}{30}-\dfrac{5}{30}=\dfrac{1}{30}\)

\(\dfrac{1}{6}-\dfrac{1}{7}=\dfrac{7}{42}-\dfrac{6}{42}=\dfrac{1}{42}\)

`@mt`

Đáp án : 

`-1/2` 

Giải thích các bước giải : 

`1/2` - (`1/3` + `2/3`) 

= `1/2` -  1 

= `-1/2` 

________________________

Đáp án : 

`7/9` 

Giải thích các bước giải : 

`4/9` + `1/2` . `2/3` 

= `4/9` + `1/3` 

= `12/27` + `9/27` 

= `21/27` = `7/9` 

.

=3/2*7/3+4/3*1/2

=21/6+4/6=25/6

\(\dfrac{11}{2}.\dfrac{21}{3}+\dfrac{11}{3}.\dfrac{1}{2}\) 

\(=\dfrac{77}{2}+\dfrac{11}{6}=\dfrac{121}{3}\)

ủa z là đáp án nào đúng trùi