\(\dfrac{2}{3}:\dfrac{4}{3}:\dfrac{5}{4}:\dfrac{1}{5}\)

=\(\dfrac{2}{3}\cdot\dfrac{3}{4}:\dfrac{5}{4}\cdot\dfrac{5}{1}\)

=\(\dfrac{1}{2}\cdot\dfrac{25}{4}\)

=\(\dfrac{25}{8}\)

\(\dfrac{1}{4}+\dfrac{2}{5}+\dfrac{3}{4}+\dfrac{3}{5}\)
\(=\left(\dfrac{1}{4}+\dfrac{3}{4}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)\)
\(=1+1\)
\(=2\)

`1/4+2/5+3/4+3/5`

`=(1/4+3/4)+(2/5+3/5)`

`=4/4+5/5`

`=1+1`

`=2`

= ( 1/4 + 3/4 ) + ( 2/5 + 3/5 ) 

= 1 + 1

= 2

\(\frac{3}{4}+\frac{2}{5}+\frac{1}{4}+\frac{3}{5}\)

\(\Leftrightarrow\left(\frac{3}{4}+\frac{1}{4}\right)+\left(\frac{2}{5}+\frac{3}{5}\right)\)

\(=1+1\)

\(=2\)

\(\frac{3}{4}+\frac{2}{5}+\frac{1}{4}+\frac{3}{5}.\)

\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\left(\frac{2}{5}+\frac{3}{5}\right)\)

\(=\frac{4}{4}+\frac{5}{5}\)

\(=1+1\)

\(=2\)

\(\frac{3}{4}+\frac{2}{5}+\frac{1}{4}+\frac{3}{5}\)

\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\left(\frac{2}{5}+\frac{3}{5}\right)\)

\(=1+1\)

\(=2\)

`4/6 xx 1/5 + 4/6 xx 3/5 + 2/6 xx 4/5`

`= 4/6 xx (1/5 + 3/5) + 2/6 xx 4/5`

`= 4/6 xx 4/5 + 2/6 xx 4/5`

`= (4/6 +2/6) xx 4/5`

`= 6/6 xx 4/5`

`=1 xx 4/5`

`=4/5`

Em cảm ơn

Có số số hạng là:

( 300- 1) : 1+ 1 = 300

Tổng dãy số trên là:

( 300+ 1) x 300 : 2 = 45150

               Đáp số: 45150

\(...=\left(300-1+1\right)\left(1+300\right):2=300.301:2=150.301=45150\)

= 3/2 + 2/3 + 2/4 + 2/5

= (6/4 + 2/4) + (2/3 + 2/5)

= 8/4 + 16/ 15 

= 46/15

=46/15

\(\frac{3}{1\times2}+\frac{3}{2\times3}+...+\frac{3}{5\times6}\)

\(=3\left(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{5\times6}\right)\)

\(=3\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}\right)\)

\(=3\left(1-\frac{1}{6}\right)=3\times\frac{5}{6}=\frac{5}{2}\)

=> S=3(1/1*2+1/2*3+...........+1/5*6

=>S=3*(1-1/6)

=>S=3*5/6

=>S=5/2

 đúng 100%

\(45150\)

Số số hạng là :

  \(\dfrac{\left(300\right)}{1}+1=300\left(SSH\right)\)

Tổng dãy số trên là :

  \(\dfrac{\left(300+1\right)\times300}{2}=45150\)

  Đ/s :...

ta thấy tổng này có \(300\) số 

tổng của 300 số đó là : \(\dfrac{\left(1+300\right)\times300}{2}=45150\)