\(x=\dfrac{4}{27}-\dfrac{2}{3}\)

\(x=-\dfrac{14}{27}\)

\(x=\dfrac{4}{27}-\dfrac{2}{3}\)

\(x=-\dfrac{14}{27}\)

\(\left(\dfrac{1}{2^2}-1\right)\times\left(\dfrac{1}{3^2-1}\right)\times\left(\dfrac{1}{4^2}-1\right)\times...\times\left(\dfrac{1}{100^2}-1\right)\)

\(=\dfrac{3}{2^2}\times\dfrac{8}{3^2}\times\dfrac{15}{4^2}\times...\times\dfrac{100^2-1}{100^2}\)

\(=\dfrac{1\times3}{2\times2}\times\dfrac{2\times4}{3\times3}\times\dfrac{3\times5}{4\times4}\times...\times\dfrac{99\times101}{100\times100}\)

\(=\dfrac{1\times2\times3\times...\times99}{2\times3\times4\times...\times100}\times\dfrac{3\times4\times5\times...\times101}{2\times3\times4\times...\times100}\)

\(=\dfrac{1}{100}\times\dfrac{101}{2}\)

\(=\dfrac{101}{200}\)

\(\left(\dfrac{1}{2^2}-1\right)\cdot\left(\dfrac{1}{3^2}-1\right)\cdot...\cdot\left(\dfrac{1}{100^2}-1\right)\)

\(=\dfrac{-3}{4}\cdot\dfrac{-8}{3}\cdot...\cdot\dfrac{-9999}{10000}\)

\(=\dfrac{1\cdot\left(-3\right)}{2\cdot2}\cdot\dfrac{2\cdot\left(-4\right)}{3\cdot3}\cdot...\cdot\dfrac{99\cdot\left(-101\right)}{100\cdot100}\)

\(=\dfrac{1\cdot2\cdot3\cdot...\cdot99}{2\cdot3\cdot4\cdot...\cdot100}\cdot\dfrac{\left(-3\right)\cdot\left(-4\right)\cdot...\cdot\left(-101\right)}{2\cdot3\cdot4\cdot...\cdot100}\)

Ở tử số phân số bên phải có số thừa số là: \(101-3+1=99\)

99 là số lẻ nên tử số vế phải sẽ cho ra số âm.

\(=\dfrac{1\cdot2\cdot3\cdot...\cdot99}{2\cdot3\cdot4\cdot...\cdot100}\cdot\dfrac{3\cdot4\cdot5\cdot...\cdot\left(-101\right)}{2\cdot3\cdot4\cdot...\cdot100}\)

\(=\dfrac{1\cdot\left(-101\right)}{100\cdot2}\)

\(=\dfrac{-101}{200}\)

chắc đéo biết

pro tìm ra x rồi còn j

\(x=\dfrac{3}{5}-\dfrac{7}{8}=-\dfrac{11}{40}\)

x = 3/5 - 7/8

x =  -11/40

x = 3/4

\(x=\dfrac{5}{8}+\dfrac{1}{8}\)

\(x=\dfrac{6}{8}=\dfrac{3}{4}\)

a, \(\dfrac{x-1}{21}\) = \(\dfrac{3}{x+1}\)

   ( x-1)(x+1) = 21.3

    x² + x - x -1 = 63

     x²                = 63 + 1

     x²               = 64

    x = + - 8

b, 2\(\dfrac{1}{2}\)x + x = 2\(\dfrac{1}{17}\)

        x( \(\dfrac{5}{2}\) + 1) = \(\dfrac{35}{17}\)

       x              = \(\dfrac{35}{17}\) : ( \(\dfrac{5}{2}\)+1)

       x             = \(\dfrac{35}{17}\) x \(\dfrac{2}{7}\)

       x            = \(\dfrac{10}{17}\)

c, (x + \(\dfrac{1}{4}\) - \(\dfrac{2}{3}\) ) : ( 2 + \(\dfrac{1}{6}\) - \(\dfrac{1}{4}\)) = \(\dfrac{7}{46}\)

   (x  - \(\dfrac{5}{12}\)):  \(\dfrac{23}{12}\)                     =   \(\dfrac{7}{46}\)

  (x - \(\dfrac{5}{12}\))                               =   \(\dfrac{7}{46}\) x \(\dfrac{23}{12}\)

  x   - \(\dfrac{5}{12}\)                                =    \(\dfrac{7}{12}\)

 x                                            =    \(\dfrac{7}{12}\) + \(\dfrac{5}{12}\)

x                                             =     1

d, 2\(\dfrac{1}{3}\)x - 1\(\dfrac{3}{4}\)x + \(2\dfrac{2}{3}\)  = 3\(\dfrac{3}{5}\)

   x( \(\dfrac{7}{3}\) - \(\dfrac{7}{4}\)) + \(\dfrac{8}{3}\)      =  \(\dfrac{18}{5}\)

   x\(\dfrac{7}{12}\)                    = \(\dfrac{18}{5}\) - \(\dfrac{8}{3}\)

   x\(\dfrac{7}{12}\)                   = \(\dfrac{14}{15}\)

  x                         = \(\dfrac{14}{15}\) : \(\dfrac{7}{12}\)

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

Phân số \(\dfrac{1}{4}\) ở trên là mình viết nhầm nhé. thực ra đề bài không có phân số này 😅

N=1/2+1/2²+...+1/2¹⁰

2N=1+1/2+...+1/2⁹

2N-N=1-1/2¹⁰=1-1/1024=1023/1024

Giải:

N=1/2+1/2²+1/2³+...+1/2⁹+1/2¹⁰

2N=1+1/2+1/2²+...+1/2⁸+1/2⁹

2N-N=(1+1/2+1/2²+...+1/2⁸+1/2⁹)-(1/2+1/2²+1/2³+...+1/2⁹+1/2¹⁰)

N=1-1/2¹⁰=1023/1024

Chúc bạn học tốt!