c) \(\left(11+12+13+...+19\right).\left(6.8-48\right)=\left(11+12+13+...+19\right).\left(48-48\right)\)

                                                                                         \(=\left(11+12+13+...+19\right).0\)

                                                                                         \(=0\)

Hok "tuốt" nha^^

b) \(\left(500.9-250.18\right).\left(1+2+3+...+9\right)=\left(250.2.9-250.18\right).\left(1+2+...+9\right)\)

                                                                                             \(=\left(250.18-250.18\right).\left(1+2+3+...+9\right)\)

                                                                                             \(=0.\left(1+2+3+...+9\right)\)

                                                                                             \(=0\)

Hok tốt nha^^ (lần 2)

a; 

c; \(\dfrac{1}{10}\) + \(\dfrac{4}{20}\) + \(\dfrac{9}{30}\)+\(\dfrac{16}{40}+\dfrac{25}{50}+\dfrac{36}{60}+\dfrac{49}{70}+\dfrac{64}{80}+\dfrac{81}{90}\)

= \(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)

= \(\dfrac{1+2+3+4+5+6+7+8+9}{10}\)

=  \(\dfrac{\left(1+9\right)+\left(2+8\right)+\left(3+7\right)+\left(4+6\right)+5}{10}\)

= \(\dfrac{10+10+10+10+5}{10}\)

= \(\dfrac{\left(10+10+10+10\right)+5}{10}\)

= \(\dfrac{10\times4+5}{10}\)

= \(\dfrac{45}{10}\)

= \(\dfrac{9}{2}\)

Phần A hình như sai đầu bài , mình sửa lại và làm luôn nhé :

A = ( 2 + 4 + 6 + 8 .... + 100 ) x ( 142142 x 143 - 143143  x 142 )

A = ( 2 + 4 + 6 + 8 + ... + 100 ) x ( 142 x 1001 x 143 - 143 x 1001 x 142 )

A = ( 2 + 4 + 6 + 8 + .. + 100 ) x 0

A = 0

B = ( 630 - 315 x 2 ) : ( 1 + 2 + 3 + ... + 1000 )

B = ( 630 - 630 ) : ( 1 + 2 + 3 + ... + 100 )

B = 0 : ( 1 + 2 + 3 + ... + 100 )

B = 0 

bài 1

a, X/Y x 1/5=3/10

X/Y=3/10:1/5

X/Y=3/2

b, 3/4 x X/Y= 6/5

X/Y=3/4:6/5

X/Y=5/8

Bài 2:

a, >     b, <       c,=        d,<

Bài 1:

a; (\(\dfrac{1}{4}\)\(x\) - \(\dfrac{1}{8}\)) x \(\dfrac{3}{4}\) = \(\dfrac{1}{4}\)

     \(\dfrac{1}{4}x\) - \(\dfrac{1}{8}\) = \(\dfrac{1}{4}\) : \(\dfrac{3}{4}\)

      \(\dfrac{1}{4}\)\(x\) - \(\dfrac{1}{8}\) = \(\dfrac{1}{4}\) x \(\dfrac{4}{3}\)

    \(\dfrac{1}{4}x\) - \(\dfrac{1}{8}\) =  \(\dfrac{1}{3}\)

      \(\dfrac{1}{4}x\) = \(\dfrac{1}{3}\) + \(\dfrac{1}{8}\)

       \(\dfrac{1}{4}\) \(x\)=  \(\dfrac{8}{24}\) + \(\dfrac{11}{24}\)

          \(\dfrac{1}{4}x=\dfrac{11}{24}\)

           \(x=\dfrac{11}{24}:\dfrac{1}{4}\)

           \(x=\dfrac{11}{24}\times4\)

           \(x=\dfrac{11}{6}\) 

b; \(\dfrac{12}{5}:x\) = \(\dfrac{14}{3}\) x \(\dfrac{4}{7}\)

     \(\dfrac{12}{5}\) : \(x\) = \(\dfrac{8}{3}\)

            \(x\) = \(\dfrac{12}{5}\) : \(\dfrac{8}{3}\)

            \(x\) = \(\dfrac{12}{5}\) x \(\dfrac{3}{8}\)

             \(x\) = \(\dfrac{9}{10}\)

Ta có công thức:

\(1-\frac{3}{n\left(n+2\right)}\)

\(=\frac{n\left(n+2\right)-3}{n\left(n+2\right)}\)

\(=\frac{n^2+2n-3}{n\left(n+2\right)}=\frac{\left(n+3\right)\left(n-1\right)}{n\left(n+2\right)}\)

Ta có: \(A=\left(1-\frac38\right)\times\left(1-\frac{3}{15}\right)\times\ldots\times\left(1-\frac{3}{143}\right)\)

\(=\left(1-\frac{3}{2\times4}\right)\times\left(1-\frac{3}{3\times5}\right)\times\ldots\times\left(1-\frac{3}{11\times13}\right)\)

\(=\frac{\left(2+3\right)\left(2-1\right)}{2\times\left(2+2\right)}\times\frac{\left(3+3\right)\left(3-1\right)}{3\times\left(3+2\right)}\times\ldots\times\frac{\left(11+3\right)\times\left(11-1\right)}{11\times\left(11+2\right)}\)

\(=\frac{5\cdot6\cdot..\cdot14}{4\cdot5\cdot..\cdot13}\cdot\frac{1\cdot2\cdot\ldots\cdot10}{2\cdot3\cdot\ldots\cdot11}=\frac{14}{4}\cdot\frac{1}{11}=\frac72\cdot\frac{1}{11}=\frac{7}{22}\)

a, = 1 - 1/2  + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9

= 1 - 1/9

= 8/9

b và c biến tử = hiệu giữa 2 thừa số ở mẫu rồi làm như a