Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2011}{2013}\div2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2011}{4026}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2011}{4026}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2013}\)
\(\Leftrightarrow x=2013-1=2012\)
Cái này lớp 6 :
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+......+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+....+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{x\left(x+1\right)}\right)=\frac{2011}{2013}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
<=> \(\frac{1}{2}-\frac{1}{x+1}=\frac{2011}{4026}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2011}{4026}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{2}{4026}=\frac{1}{2013}\)
\(\Leftrightarrow x+1=2013\)
=> x = 2012
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2011}{2013}\)
\(\Rightarrow2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2011}{2013}\)
\(\Rightarrow2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2011}{2013}\)
\(\Rightarrow2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
\(\Rightarrow2.\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2011}{2013}\)
\(\Rightarrow1-\frac{2}{x+1}=\frac{2011}{2013}\)
\(\Rightarrow\frac{2}{x+1}=1-\frac{2011}{2013}\)
\(\Rightarrow\frac{2}{x+1}=\frac{2}{2013}\)
\(\Rightarrow x+1=2013\)
\(\Rightarrow x=2013-1\)
\(\Rightarrow x=2012\)
Vậy \(x=2012\)
~ Ủng hộ nhé
= ( 2011 * 2012 + 2012 * 2013 ) : ( 1/3 - 1/2 : 3/2 )
= ( 2011 * 2012 + 2012 * 2013 ) : ( 1/3 - 1/3 )
= ( 2011 * 2012 + 2012 * 2013 ) : 0 ( không chia được cho số 0 )
Bài toán không có kết quả
\(x+\frac{3+\frac{3}{20}+\frac{3}{13}+\frac{3}{2013}}{5+\frac{5}{20}+\frac{5}{13}+\frac{5}{2013}}=\frac{9}{2}\)
\(x+\frac{3\times\left(1+\frac{1}{20}+\frac{1}{13}+\frac{1}{2013}\right)}{5\times\left(1+\frac{1}{20}+\frac{1}{13}+\frac{1}{2013}\right)}=\frac{9}{2}\)
\(x+\frac{3}{5}=\frac{9}{2}\)
\(x=\frac{39}{10}\)
\(x=3,9\)
\(\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x...x\left(1-\frac{1}{2014}\right)\)
A = \(\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{2012}{2013}x\frac{2013}{2014}\)
A = \(\frac{2x3x4x...x2012x2013}{3x4x5x...x2013x2014}\)
a = \(\frac{2}{2014}=\frac{1}{1007}\)
3 + \(\frac{3}{20}\)+ \(\frac{3}{13}\) + \(\frac{3}{2013}\)
X x = \(\frac{5}{3}\)
5 + \(\frac{5}{20}\) + \(\frac{5}{13}\) + \(\frac{5}{2013}\)
3 x ( 1 + \(\frac{1}{20}\) + \(\frac{1}{13}\) + \(\frac{1}{2013}\) )
X x = \(\frac{5}{3}\)
5 x ( 1 + \(\frac{1}{20}\) +\(\frac{1}{13}\) + \(\frac{1}{2013}\) )
X x \(\frac{3}{5}\) = \(\frac{5}{3}\) => X = \(\frac{25}{9}\) vậy X = \(\frac{25}{9}\)
Ta có : \(X.\frac{3+\frac{3}{20}+\frac{3}{13}+\frac{3}{2013}}{5+\frac{5}{20}+\frac{5}{13}+\frac{5}{2013}}=\frac{5}{3}\)
\(\Leftrightarrow X.\frac{3\left(1+\frac{1}{20}+\frac{1}{13}+\frac{1}{2013}\right)}{5\left(1+\frac{1}{20}+\frac{1}{13}+\frac{1}{2013}\right)}=\frac{5}{3}\)
\(\Leftrightarrow X.\frac{3}{5}=\frac{5}{3}\Rightarrow X=\frac{5}{3}:\frac{3}{5}=\frac{5}{3}.\frac{5}{3}=\frac{25}{9}\)
\(\frac{75}{20-x}=\frac{3}{2}.10\)
\(\frac{75}{20-x}=15\)
\(\Rightarrow\left(20-x\right).15=75\)
\(\Rightarrow20-x=75:15\)
\(\Rightarrow20-x=5\)
\(\Rightarrow x=15\)
vậy \(x=15\)
\(2013x-x=2013.2011+2013\)
\(2012x=2013\left(2011+1\right)\)
\(2012x=2013.2012\)
\(x=2013\)
vậy \(x=2013\)
\(\left(x-15\right).7=270:45\)
\(\left(x-15\right).7=6\)
\(x-15=\frac{6}{7}\)
\(x=\frac{6}{7}+15\)
\(x=\frac{111}{7}\)
vậy \(x=\frac{111}{7}\)
\(\left(x-15\right).7=169\)
\(x-15=\frac{169}{7}\)
\(x=\frac{169}{7}+15\)
\(x=\frac{274}{7}\)
vậy \(x=\frac{274}{7}\)
thông cảm đề bài câu cuối ko hiểu