Ta có: A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 18.19.20
=> 4A = 4(1.2.3 + 2.3.4 + 3.4.5 + ... + 18.19.20)
=> 4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 +...... +18.19.20.4
=> 4A = 1.2.3.4 + 2.3.4(5 - 1) + 3.4.5.(6 - 2) +..... +18.19.20.(21 - 17)
=> 4A = 1.2.3.4 + 2.3.4.5 - 2.3.4 + 3.4.5.6 - 2.3.4.5 + ..... + 17.18.19.20 - 17.18.19.20
=> 4A =18.19.20
=> 4A = 6840
=> A = 1710

Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+18.19.20

4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+18.19.20)4

4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+18.19.20.(21-17)

4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+ 18.19.20.21-17.18.19.20
=>A =18.19.20.21

=>A+18.19.20.21/4

=> A=35910

1/2-(4/12+9/12)<x<1/24-(3/24-8/24)

1/2-13/12<x<1/24-(-5/24)

-7/12<x<1/4

=>x\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) E{0}

ta có:\(\frac{1}{2}-\left(\frac{1}{3}+\frac{3}{4}\right)=\frac{-1}{12}=-0,08333333\)

mà \(\frac{1}{24}-\left(\frac{1}{8}-\frac{1}{3}\right)=\frac{1}{4}=0.25\)

nên suy ra không có số nguyên x nào thỏa mãn đề bài.

Sao ai cũng giải khó hiểu thế vậy trời:))

     Bài 1:

\(x\) \(\times\) \(\dfrac{15}{16}\) - \(x\) \(\times\) \(\dfrac{4}{16}\) = 2

\(x\) \(\times\) (\(\dfrac{15}{16}\) - \(\dfrac{4}{16}\)) = 2

\(x\) \(\times\) \(\dfrac{11}{16}\) = 2

\(x\) = 2 : \(\dfrac{11}{16}\)

\(x\) = 2 x \(\dfrac{16}{11}\)

\(x\) = \(\dfrac{32}{11}\)

Bài 2: 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + ... + \(\dfrac{1}{x\left(x+1\right):2}\) = 1 : \(\dfrac{2011}{2012}\)

1 + 2\(\times\) ( \(\dfrac{1}{2\times3}\) + \(\dfrac{1}{2\times6}\) + \(\dfrac{1}{2\times10}\) + ... + \(\dfrac{2}{2\times x\times\left(x+1\right)}\)) = \(\dfrac{2012}{2011}\)

1 + 2 \(\times\)(\(\dfrac{1}{2\times3}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\)+...+ \(\dfrac{1}{x\times\left(x+1\right)}\)) = \(\dfrac{2012}{2011}\)

1 + 2 \(\times\) (\(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\) + ... + \(\dfrac{1}{x\times\left(x+1\right)}\)) = 1 + \(\dfrac{1}{2011}\)

1 + 2\(\times\)(\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + ... + \(\dfrac{1}{x}\) - \(\dfrac{1}{x+1}\)) = 1 + \(\dfrac{1}{2011}\)

 1 + 2 \(\times\) (\(\dfrac{1}{2}\) - \(\dfrac{1}{x+1}\)) = 1 + \(\dfrac{1}{2011}\)

  1 + 1 - \(\dfrac{2}{x+1}\) = 1 + \(\dfrac{1}{2011}\)

    \(\dfrac{2}{x+1}\) = 1 + 1 - 1  - \(\dfrac{1}{2011}\)

    \(\dfrac{2}{x+1}\) =  2 - 1 - \(\dfrac{1}{2011}\)

  \(\dfrac{2}{x+1}\)  = 1 - \(\dfrac{1}{2011}\)

     \(\dfrac{2}{x+1}\) = \(\dfrac{2010}{2011}\)

       \(x\) + 1 = 2 : \(\dfrac{2010}{2011}\)

        \(x\) + 1 = \(\dfrac{2011}{1005}\)

         \(x\) = \(\dfrac{2011}{1005}\) - 1  = \(\dfrac{1006}{1005}\)(loại vì \(\dfrac{1006}{1005}\) không phải là số tự nhiên)

Vậy không có giá trị nào của \(x\) là số tự nhiên thỏa mãn đề bài. 

Bài 3:

\(\dfrac{x}{16}\) \(\times\) (2017 - 1) = 2

\(\dfrac{x}{16}\) \(\times\) 2016 = 2

 \(\dfrac{x}{16}\)             = 2 : 2016

 \(\dfrac{x}{16}\)            = \(\dfrac{1}{1008}\)

   \(x\)             = \(\dfrac{1}{1008}\) x 16

  \(x\) = \(\dfrac{1}{63}\)

( 1-1/2) . (1-1/3).(1-1/4).......(1-1/2016) . (1-1/2017)

=1/2.2/3.3.4x...x2015/2016.2016/2017

=1.2.3.4. ... .2015.2016/2.3.4.5. ... .2016.2017

(giống nhau bạn gạch đi )

=1/2017

 ( 1-1/2) . (1-1/3).(1-1/4).......(1-1/2016) . (1-1/2017)

=1/2 . 2/3 . 3/4 ......... 2015/2016  .  2016/2017

=1.2 .3......2015.2016/2.3.4.......2016.2017

=1/2017

 =1/2 * 2/3 * 3/4 * ... * 2016/2017

= 1/2017

\(A=\frac{2}{3}+\frac{1}{3}+\frac{1}{15}+\frac{1}{75}+\frac{1}{375}+\frac{1}{1875}\)

\(A=\left(\frac{2}{3}+\frac{1}{3}\right)+\frac{1}{15}+\frac{1}{75}+\frac{1}{375}+\frac{1}{1875}\)

\(A=1+\left(\frac{5}{75}+\frac{1}{75}\right)+\frac{1}{375}+\frac{1}{1875}\)

\(A=1+\frac{6}{75}+\frac{1}{375}+\frac{1}{1875}\)

\(A=1+\left(\frac{150}{1875}+\frac{1}{1875}\right)+\frac{1}{375}\)

\(A=1+\frac{151}{1875}+\frac{1}{375}\)

\(A=1+\left(\frac{151}{1875}+\frac{5}{1875}\right)\)

\(A=1+\frac{156}{1875}\)

\(A=\frac{1875}{1875}+\frac{156}{1875}\)

\(A=\frac{677}{625}\)

\(A=\frac{2}{3}+\frac{1}{3}+\frac{1}{15}+\frac{1}{75}+\frac{1}{375}+\frac{1}{1875}\)

\(\Leftrightarrow A=\left(\frac{2}{3}+\frac{1}{3}\right)+\left(\frac{1}{15}+\frac{1}{75}\right)+\left(\frac{1}{375}+\frac{1}{1875}\right)\)

\(\Leftrightarrow A=1+\left(\frac{5}{75}+\frac{1}{75}\right)+\left(\frac{5}{1875}+\frac{1}{1875}\right)\)

\(\Leftrightarrow A=1+\frac{6}{75}+\frac{6}{1875}\)

\(\Leftrightarrow A=1+\frac{2}{25}+\frac{2}{625}\)

\(\Leftrightarrow A=1+\left(\frac{2}{25}+\frac{2}{625}\right)\)

\(\Leftrightarrow A=1+\left(\frac{50}{625}+\frac{2}{625}\right)\)

\(\Leftrightarrow A=1+\frac{52}{625}\)

\(\Leftrightarrow A=\frac{677}{625}\)

=\(\frac{677}{625}\)

a) B = 5/16 : 0,125 - ( 9/4 - 0,6 ) * 10/11

B = 5/16 * 8 - 9/4 * 10/11 + 0,6 * 10/11

B = 5/2 - 45/22 + 3/11

B = 55/22 - 45/22 + 6/22

B = 8/11

b) \(\left(\frac{1}{2}+1\right)\left(\frac{1}{3}+1\right).....\left(\frac{1}{99}+1\right)\)

\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.....\frac{100}{99}\)

\(=\frac{3.4.5.....100}{2.3.4.....99}\)

\(=\frac{\left(3.4.....99\right).100}{2\left(3.4.....99\right)}\)

\(=\frac{100}{2}\)

\(=50\)

a)B= 5/6 : 1/8 - (9/4 - 3/5 ) * 10/11

= 5/2 - 33/20 * 10/11

= 5/2 - 3/2

= 1

b) 3/2.4/3.5/4....100/99

= 3.4.5...100/2.3.4...99

=100/2

=50