1 1 /5 x 1 1/6 x 1 1/7 x .....x 1 1/ 2009
ai nhanh mình có quà
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XO
14 tháng 8 2019
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\times\left(x+1\right):2}=\frac{2011}{2013}\)
\(\Rightarrow\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\times\left(x+1\right)}\times\frac{1}{2}=\frac{2011}{2013}\)
\(\Rightarrow2\times\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\times\left(x+1\right)}\right)=\frac{2011}{2013}\)
\(\Rightarrow2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{x\times\left(x+1\right)}\right)=\frac{2011}{2013}\)
\(\Rightarrow2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
\(\Rightarrow2\times\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2011}{2013}:2\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2011}{4026}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2011}{4016}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2013}\)
\(\Rightarrow x+1=2013\)
\(\Rightarrow x=2012\)
Vậy x = 2012
4 tháng 8 2018
\(a,-12\left(x-5\right)+7\left(3-x\right)=5\)
\(-12x+60+21-7x=5\)
\(-12x-7x+81=5\)
\(-19x=5-81\)
\(-19x=-76\)
\(x=-76:\left(-19\right)\)
\(x=4\)
\(Vậyx=4\)
\(b,30\left(x+2\right)-6\left(x-5\right)-24x=100\)
\(30x+60-6x-30-24x=100\)
\(30x-6x-24x+60-30=100\)
\(0x+30=100\)
\(\Rightarrow Vôlý\)
Vậy không có giá trị nào của x thỏa mãn đề bài.
\(c,-5\left(x+\frac{1}{5}\right)-\frac{1}{2}\left(x-\frac{2}{3}\right)=\frac{3}{2}x-\frac{5}{6}\)
\(-5x-1-\frac{1}{2}x-\frac{1}{3}=\frac{3}{2}x-\frac{5}{6}\)
\(-5x-\frac{1}{2}x-1-\frac{1}{3}=\frac{3}{2}x-\frac{5}{6}\)
\(-\frac{11}{2}x-\frac{2}{3}=\frac{3}{2}x-\frac{5}{6}\)
\(-\frac{2}{3}+\frac{5}{6}=\frac{3}{2}x+\frac{11}{2}x\)
\(-\frac{4}{6}+\frac{5}{6}=\frac{14}{2}x\)
\(\frac{1}{6}=7x\)
\(x=\frac{1}{6}:7\)
\(x=\frac{1}{6}.\frac{1}{7}\)
\(x=\frac{1}{42}\)
\(Vậyx=\frac{1}{42}\)
\(d,-3\left(x-\frac{1}{2}\right)-5\left(x+\frac{3}{5}\right)=-x+\frac{1}{5}\)
\(-3x+\frac{3}{2}-5x-3=-x+\frac{1}{5}\)
\(-3x-5x+\frac{3}{2}-3=-x+\frac{1}{5}\)
\(-8x+\frac{3}{2}-\frac{6}{2}=-x+\frac{1}{5}\)
\(-8x-\frac{3}{2}=-x+\frac{1}{5}\)
\(-\frac{3}{2}-\frac{1}{5}=-x+8x\)
\(\frac{15}{10}-\frac{2}{10}=7x\)
\(7x=\frac{13}{10}\)
\(x=\frac{13}{10}:7\)
\(x=\frac{13}{10}.\frac{1}{7}\)
\(x=\frac{13}{70}\)
\(Vậyx=\frac{13}{70}\)
14 tháng 5 2023
\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)
\(=1-\dfrac{1}{8}=\dfrac{7}{8}\)
13 tháng 6 2018
1/ X : 1/7 + 1/7 = 8/9
X : 1/7 = 8/9 -1/7
X : 1/7 = 47/63
X = 47/63 x 1/7
X = 47/441
2/ X : ( 1/7 + 6/7 ) = 8/9
X : 1 = 8/9
X = 8/9 x1
X = 8/9
3/ 1/7 : ( X + 4/7 ) = 13/5
X + 4/7 = 1/7 : 13/5
X + 4/7 = 5/91
X = 5/91 - 4/7
X = -49/91
4/ 3/7 : ( X - 1/9) = 4/5
X - 1/9 = 3/7 : 4/5
X -1/9 = 15/28
X = 15/28 + 1/9
X = 163/252
3 tháng 2 2017
5 ( x - 1 ) - 6 ( x + 1 ) = 7
5x - 5 - 6x - 6 = 7
( 5 - 6)x - 11 = 7
(-1)x = 7 + 11
(-1)x = 18
x = 18 : ( -1 )
x = -18
b ) 4 ( x - 1 ) + 5 ( 1 - x ) = -17
4x - 4 + 5 - 5x = -17
( 4 - 5 )x + 1 = -17
(-1)x = -17 - 1 = -18
x = -18 : (-1 )
x = 18
k nha >-< ???
15 tháng 4 2021
a, \(\dfrac{3}{15}-x=-\dfrac{1}{7}\Leftrightarrow\dfrac{21-105x}{105}=\dfrac{-15}{105}\Rightarrow-105x=-36\)
\(\Leftrightarrow x=\dfrac{36}{105}=\dfrac{12}{35}\)
b, \(\left(4,5+\dfrac{3}{4}x\right):\dfrac{8}{3}=\dfrac{9}{3}\Leftrightarrow\dfrac{45}{10}+\dfrac{3x}{4}=\dfrac{72}{9}=8\)
\(\Leftrightarrow\dfrac{36}{4}+\dfrac{3x}{4}=\dfrac{32}{4}\Rightarrow3x=-4\Leftrightarrow x=-\dfrac{4}{3}\)
c, mình ko hiểu đề lắm
\(=\frac{6}{5}x\frac{7}{6}x\frac{8}{7}x...x\frac{2009}{2008}x\frac{2010}{2009}=\frac{2010}{5}=402\)