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THANKS

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{x\cdot\left(x+1\right)}=2\)

\(\Leftrightarrow\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{x\cdot\left(x+1\right)}=2\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+1}=2\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=2\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-2\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{-3}{2}\)

\(\Leftrightarrow\frac{-3}{-3x-3}=\frac{-3}{2}\)

\(\Leftrightarrow-3x-3=2\)

\(\Leftrightarrow-3x=2+3\)

\(\Leftrightarrow-3x=5\)

\(\Leftrightarrow x=\frac{-5}{3}\)

Vậy \(x=\frac{-5}{3}\)

\(\frac{1}{x}+\frac{1}{2.x}+\frac{1}{6x}+\frac{1}{12x}+\frac{1}{30x}\)

= \(\frac{1}{x}\left(1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}\right)\)

= \(\frac{1}{x}\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)

= \(\frac{1}{x}\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)

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

=\(\frac{1}{x}.\frac{11}{6}\)

=\(\frac{11}{6x}\)

41/42 - 1/2 - 1/6 - 1/12 - 1/20 -1/30 = 1/x

1/7 = 1/x

x = 1 / 1/7

x = 7

chi lớp 4 há

                          \(\frac{1}{1X2}+\frac{1}{2X3}+\frac{1}{3X4}+\frac{1}{4X5}+\frac{1}{5X6}+\frac{1}{x}\)=    \(\frac{41}{42}\)

                            \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{x}=\frac{41}{42}\)

                             \(1-\frac{1}{6}+\frac{1}{x}=\frac{41}{42}\)

                            \(\frac{5}{6}+\frac{1}{x}=\frac{41}{42}\)     

                                             \(\frac{1}{x}\)     =\(\frac{41}{42}-\frac{5}{6}\) 

                                              \(\frac{1}{x}\)    =   \(\frac{1}{7}\)        

                         VẬy x = 7

                       k cho mik nha

1/2 + 1/6 + 1/12 + 1/20 + 1/30 1/x = 41/42

5/6 + 1/x = 41/42

1/x = 41/42 - 5/6 

1/x = 1/7 

vậy x = 7

x = 7 ở vong 18 đúng không

chuẩn 

đề lạ thế

x + 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 = 1 

x + 1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + 1/5*6 + 1/6*7 = 1 

x + 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 = 1 

x + 1/1 - 1/7 = 1 

x + 6/7 = 1 

x = 1 - 6/7 

x = 1/7 

x + 1/2 + 1/6 + 1/20 + 1/30 + 1/42 = 1

x + 65/84 = 1

x = 1 - 65/84

x = 19/84

x + 1/2 + 1/6 + 1/12 + 1/20 + 1/30 × 1/42 = 1

<=> x + 6/7 = 1

<=> x = 1 - 6/7

<=> x = 1/7

 Vậy x = 1/7

bằng 7 dúng không

\(\frac{1}{x}=\frac{41}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(\frac{1}{x}=\frac{1}{7}=>x=7\)

Lời giải:

$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{x(x+1)}=\frac{3}{8}$

$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{x(x+1)}=\frac{3}{8}$

$1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-.....+\frac{1}{6}-\frac{1}{7}+\frac{1}{x(x+1)}=\frac{3}{8}$

$1-\frac{1}{7}+\frac{1}{x(x+1)}=\frac{3}{8}$
$\frac{6}{7}+\frac{1}{x(x+1)}=\frac{3}{8}$

$\frac{1}{x(x+1)}=\frac{3}{8}-\frac{6}{7}=\frac{-27}{56}$

Kết quả này không phù hợp lắm.

Bạn xem lại đề nhé. 

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{x}=\frac{41}{42}\)

=>\(\frac{1}{x}=\frac{41}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

=>\(\frac{1}{x}=\frac{410-14-21-35-70-210}{420}\)

=>\(\frac{1}{x}=\frac{1}{7}\)

=> x = 7

K mình nhé mn !!!