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24 tháng 4 2016

* ĐK: \(x\ne0\)

Đề ra ...<=> \(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)

<=> \(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{1}{9}\)

<=> \(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

<=>\(\frac{1}{6}-\frac{1}{x+1}+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

<=>\(\frac{1}{x+1}\left(1-\frac{1}{x}\right)=\frac{1}{6}-\frac{1}{9}\)

<=> \(\frac{x-1}{x\left(x+1\right)}=\frac{1}{36}\)

<=> \(\frac{x-1}{x\left(x-1\right)}=\frac{x-1}{36.\left(x-1\right)}\)

=> x(x-1) = 36. (x-1) => x =36

24 tháng 4 2016

\(\frac{2}{2}.\left(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x+\left(x+1\right)}\right)=\frac{2}{9}\)

\(2\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{2}{9}\)

\(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x.\left(x+1\right)}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

\(\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}\)

\(\frac{1}{x+1}=\frac{1}{18}\)

x+1=18

x=18-1

x=17

24 tháng 4 2016

1/21 + 1/28 + 1/36 + ...+ 1/x(x+1)

=> 2/42 + 2/56 + 2/72 +....+ 2/x(x+1)

=> 2.(1/42 + 1/56 + 1/72 + ... + 1/x.(x+1))

=> 2 .(1/6.7 + 1/7.8 + 1/8.9 + ..+ 1/x.(x+1))

=> 2. ( 1/6 - 1/7 + 1/7-1/8 + ...+ 1/x - 1/x+1

=> 2 . (1/6 - 1/x+1)

=>1/3 - 2/x+1

18 tháng 9 2020

\(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+.......+\frac{2}{x\left(x+1\right)}=\frac{11}{40}\)

\(\Leftrightarrow\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+........+\frac{2}{x\left(x+1\right)}=\frac{11}{40}\)

\(\Leftrightarrow2.\left[\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+.......+\frac{1}{x\left(x+1\right)}\right]=\frac{11}{40}\)

\(\Leftrightarrow\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+......+\frac{1}{x\left(x+1\right)}=\frac{11}{80}\)

\(\Leftrightarrow\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+.......+\frac{1}{x\left(x+1\right)}=\frac{11}{80}\)

\(\Leftrightarrow\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+.......+\frac{1}{x}-\frac{1}{x+1}=\frac{11}{80}\)

\(\Leftrightarrow\frac{1}{5}-\frac{1}{x+1}=\frac{11}{80}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{16}\)

\(\Leftrightarrow x+1=16\)\(\Leftrightarrow x=15\)

Vậy \(x=15\)

22 tháng 4 2018

\(\frac{1}{21}+\frac{1}{28}+...+\frac{2}{x\left(x+1\right)}\)

\(=\frac{2}{42}+\frac{2}{56}+...+\frac{2}{x\left(x+1\right)}\)

\(=2\left(\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{x\left(x+1\right)}\right)\)

\(=2\left(\frac{1}{6}-\frac{1}{x+1}\right)\)

\(=2\left(\frac{x-5}{6x+6}\right)=\frac{2\left(x+5\right)}{2\left(3x+3\right)}=\frac{x+5}{3x+3}\)

10 tháng 8 2016

1/21 + 1/28 + 1/36 + ... + 2/x(x + 1) = 2/9

1/2 × (1/21 + 1/28 + 1/36 + ... + 2/x(x + 1) = 1/2 × 2/9

1/42 + 1/56 + 1/72 + ... + 1/x(x + 1) = 1/9

1/6×7 + 1/7×8 + 1/8×9 + ... + 1/x(x + 1) = 1/9

1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + ... + 1/x - 1/x + 1 = 1/9

1/6 - 1/x + 1 = 1/9

1/x + 1 = 1/6 - 1/9

1/x + 1 = 3/18 - 2/18

1/x + 1 = 1/18

=> x + 1 = 18

=> x = 18 - 1

=> x = 17

28 tháng 7 2018

=2/42+2/56+....+2/x.(x+1)

=2/6.7+2/7.8+.....+2/x.(x+1)

=2.(1/6.7-1/7.8+....+1/x.(x+1)

=2.(1/6-1/7+1/7-1/8+...+1/x-1/x+1)

=2.(1/6-1/x+1)

=2.(x-5/6x+6)

=2x-10/6x+6

bn vt thieu de nha = bao nhieu bn tu tinh