\(46\cdot99\)

\(=46\cdot\left(100-1\right)\)

\(=46\cdot100-46\)

\(=4600-46\)

\(=4554\)

___________

\(34\cdot11\)

\(=34\cdot\left(10+1\right)\)

\(=34\cdot10+34\)

\(=340+34\)

\(=374\)

___________

\(25\cdot12\) 

\(=5\cdot5\cdot12\)

\(=5\cdot60\)

\(=300\)

__________

\(15\cdot4\)

\(=15\cdot2\cdot2\)

\(=30\cdot2\)

\(=60\)

____________

\(45\cdot6\)

\(=45\cdot2\cdot3\)

\(=90\cdot3\)

\(=2700\)

________

\(13\cdot99\)

\(=13\cdot\left(100-1\right)\)

\(=13\cdot100-13\)

\(=1300-13\)

\(=1287\)

______________

\(16\cdot19\)

\(=16\cdot\left(20-1\right)\)

\(=16\cdot20-16\)

\(=320-16\)

\(=304\)

_____________

\(35\cdot98\)

\(=35\cdot\left(100-2\right)\)

\(=35\cdot100-35\cdot2\)

\(=3500-70\)

\(=3430\)

____________

\(125\cdot16\)

\(=125\cdot8\cdot2\)

\(=1000\cdot2\)

\(=2000\)

___________

\(47\cdot101\)

\(=47\cdot\left(100+1\right)\)

\(=47\cdot100+47\)

\(=4700+47\)

\(=4747\)

46 x 99 =4554  , 34 x 11 = 374 , 25 x 12 =- 300 , 15 x 4 = 60 , 45 x 6 = 270 , 13 x 99 = 1287 , 16 x 19 = 304

35 x 98 = 3430 , 125 x 16  = 2000 ,  47 x 101  = 4747

\(\dfrac{x}{3}+\dfrac{x}{15}+\dfrac{x}{35}+...+\dfrac{x}{99}=2023\times\dfrac{5}{11}\)
\(\dfrac{x}{1.3}+\dfrac{x}{3.5}+\dfrac{x}{5.7}+...+\dfrac{x}{9.11}=2023\times\dfrac{5}{11}\)
\(x-\dfrac{x}{3}+\dfrac{x}{3}-\dfrac{x}{5}+\dfrac{x}{5}-\dfrac{x}{7}+...+\dfrac{x}{9}-\dfrac{x}{11}=2023\times\dfrac{5}{11}\)
\(x-\dfrac{x}{11}=2023\times\dfrac{5}{11}\)
\(\dfrac{11\times x-x}{11}=2023\times\dfrac{5}{11}\)
\(\dfrac{10\times x}{11}=2023\times\dfrac{5}{11}\)
\(\dfrac{10}{11}\times x=2023\times\dfrac{5}{11}\)
\(x=2023\times\dfrac{5}{11}:\dfrac{10}{11}\)
\(x=\dfrac{2023}{2}=1011,5\)
#AvoidMe

= (8x15x24x35x...x99) / (9x16x25x36x...x100)

= (4x2x5x3x6x2x2x5x7x...x9x11) / (9x4x2x2x5x5x6x3x2x...x25x4)

= 11/(4x25)

= 11/100

Mình không chắc lắm

a) \(A=\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)

\(A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.10}+\dfrac{1}{143}\)

\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)+\dfrac{1}{143}\)

\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{100}\right)+\dfrac{1}{143}=\dfrac{1}{2}.\dfrac{99}{100}+\dfrac{1}{143}=\dfrac{99}{200}+\dfrac{1}{143}=\dfrac{99.143+200.1}{200.143}=\dfrac{14157+200}{28600}=\dfrac{14357}{28600}\)

b) \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+99\right)=14950\)

\(\Rightarrow x+x+...+x+\left(1+2+...+99\right)=14950\)

\(\Rightarrow100x+\left(\left(99+1\right):2\right).99:2=14950\)

\(\Rightarrow100x+2475=14950\Rightarrow100x=12475\Rightarrow x=\dfrac{12475}{100}=\dfrac{499}{4}\)

47. (23 + 50)- 23. ( 47+50 )

= 47. 23+ 47. 50- 23. 47 - 23. 50

=47. 50 - 23. 50

= 50 .( 47 -23)

=50. 24 = 1200

(-33 ). (-5) - 33 . 4 + 33

= 33 ( 5 - 4 + 1)

=33 . 2 = 66

giup minh voi 

\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+....+\frac{2}{575}+\frac{2}{675}\)

\(=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{23\times25}+\frac{2}{25\times27}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{23}-\frac{1}{25}+\frac{1}{25}-\frac{1}{27}\)

\(=\frac{1}{3}-\frac{1}{27}=\frac{8}{27}\)

Vậy ....

\(\frac{2}{15}+\frac{2}{35}+\frac{2}{69}+........+\frac{2}{575}+\frac{2}{675}\)

\(=\frac{2}{3\times5}+\frac{2}{5\times7}+........+\frac{2}{23\times25}+\frac{2}{25\times27}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.......+\frac{1}{23}-\frac{1}{25}+\frac{1}{25}-\frac{1}{27}\)

\(=\frac{1}{3}-\frac{1}{27}\)

\(=\frac{8}{27}\)

\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+...+\frac{2}{575}+\frac{2}{675}\)

\(=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+...+\frac{2}{23\times25}+\frac{2}{25\times27}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{25}+\frac{1}{25}-\frac{1}{27}\)

\(=\frac{1}{3}-\frac{1}{27}\)

\(=\frac{8}{27}\)

_Chúc bạn học tốt_

a)

Ta có : ( 1 + 2 + 3 + ... + 99)

Số số hạng là:       ( 99 - 1 )  : 1 + 1 = 100

Tổng là:                 ( 99 + 1 ) x 100 : 2 = 5000

=> 5000 x ( 13  - 12 - 1 ) x 15

=> 5000 x 10 x 15

=> 50000 x 15

=> 750000

Ko muốn vt nx :))

=1/(1x3)x1/(2x4)x...x1/(9x11)

=1/(1x3x2x4x...x9x11)

=1/(1x2x3x3x4x4x5x5x...x9x10x11)