\(B=\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+...+\dfrac{1}{1+2+3+4+...+2019}\)

\(B=\dfrac{1}{\dfrac{\left(1+2\right).2}{2}}+\dfrac{1}{\dfrac{\left(1+3\right).3}{2}}+\dfrac{1}{\dfrac{\left(1+4\right).4}{2}}+...+\dfrac{1}{\dfrac{\left(1+2019\right).2019}{2}}\)

\(B=\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+...+\dfrac{2}{2019.2020}\)

\(B=2.\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{2019.2020}\right)\)

\(B=2.\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{2019}-\dfrac{1}{2020}\right)\)

\(B=2.\left(\dfrac{1}{2}-\dfrac{1}{2020}\right)\)

\(B=1.\dfrac{1}{100}< 1\)

Vay B < 1

`x-120 : 30 =40`

`x-4=40`

`x=40+4`

`x=44`

___________________

`128-3.(x+4)=23`

`3.(x+4)=128-23`

`3.(x+4)=105`

`x+4=105:3`

`x+4=35`

`x=35-4`

`x=31`

___________________________

` 274 - ( 9 . x + 18 ) = 4`

`9x+18=274-4`

`9x+18=270`

`9x=270 - 18`

`9x=252`

`x=252:9`

`x=28`

____________________________

`x.34-x.14=200`

`34x-14x=200`

`20x=200`

`x=200:20`

`x=10`

a, x = 44

b, x = 31

c, x = 28

d, x = 1000

\(x+x.\dfrac{1}{3}+\dfrac{5}{18}=1\dfrac{1}{6}\)

`=> 2x . 1/3 + 5/18 = 7/6`

`2x . 1/3 = 7/6 - 5/18`

`2x . 1/3 = 21/18 - 5/18`

`2x . 1/3 = 8/9`

`2x=8/9 : 1/3`

`2x=8/9 .3`

`2x=8/3`

`x=8/3 : 2`

`x=8/3 . 1/2`

`x=4/3`

_________________________

`x . 2/3 -1/5 = 1 12/15`

`2/3 x - 1/5 =9/5`

`2/3 x= 9/5 + 1/5`

`2/3 x = 10/5`

`2/3 x = 2`

`x=2 : 2/3`

`x=2 .3/2`

`x=3`

______________________

`x : 1/2 : 1/6 = 2 2/5`

`x . 2 . 6 =12/5`

`x . 2 = = 12/5 : 6`

`x.2 = 12/5 .1/6`

`2x = 2/5`

`x=2/5 : 2`

`x=2/5 . 1/2`

`x=1/5`

\(\left(\dfrac{1}{25.26}+\dfrac{1}{26.27}+......+\dfrac{1}{29.30}\right).150+\dfrac{103}{100}:\left(\dfrac{103}{10}.\dfrac{1}{x-1}\right)\)

\(=\left(\dfrac{1}{25}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{27}+....+\dfrac{1}{29}-\dfrac{1}{30}\right).150+\dfrac{103}{100}:\left(\dfrac{103}{10}.\dfrac{1}{x-1}\right)\)

\(=\left(\dfrac{1}{25}-\dfrac{1}{30}\right)\)\(.150+\dfrac{103}{100}:\left(\dfrac{103}{10}.\dfrac{1}{x-1}\right)\)

\(=\dfrac{1}{150}\)\(.150+\dfrac{103}{100}:\left(\dfrac{103}{10}.\dfrac{1}{x-1}\right)\)

\(=\dfrac{150}{150}+\dfrac{103}{100}:\left(\dfrac{103}{10}.\dfrac{1}{x-1}\right)\)

\(=1+\dfrac{103}{100}:\left(\dfrac{103}{10}.\dfrac{1}{x-1}\right)\)

`=203/100 : (103/10 . 1/(x-1) )`

=>

A = 37 x 39 x 41 x 43 x ....x 2021 

A = 37 x 39 x 41 x 43 x 45 x 47x 49x..x2021

A = \(\overline{...5}\) (vì tích của thừa số có tận cùng bằng 5 với các thừa số lẻ luôn có tận cùng bằng 5 )

A = 37 x 39 x 41 x 43 x ....x 2021 

A = 37 x 39 x 41 x 43 x 45 x 47x 49x..x2021

A = $\overline{...5}$ (vì tích của thừa số có tận cùng bằng 5 với các thừa số lẻ luôn có tận cùng bằng 5 )

\(\left\{{}\begin{matrix}a+b\le10\\b\le7\end{matrix}\right.\) ⇔ \(\left\{{}\begin{matrix}b\le7\\a\le3\end{matrix}\right.\) ⇔  P ≤ 3² + 7² = 58

P(max)= 58  ⇔ a =3; b = 7

a ≥ 0; b ≥ 0 ⇔P = a² + b²≥ 0 + 0 = 0 ⇔ P(min) = 0 ⇔ a=b=0

   99999 + 9999 + 999 + 99 + 9

= 99999 + 1 + 9999 + 1 + 999 + 1 + 99 + 1  + 5

= 100000 + 10000 + 1000 + 100 + 5

 = 111105

Ta có: \(99999+9999+999+99+9\)

\(=100000-1+10000-1+1000-1+100-1+10-1\)

\(=\left(100000+10000+1000+100+10\right)-\left(1+1+1+1+1\right)\)

\(=111110-5\)

\(=111105\)