\(3-\frac{1-\frac{1}{2}}{1+\frac{1}{x}}=2\frac{2}{3}\)
\(\Leftrightarrow\frac{\frac{1}{2}}{\frac{x+1}{x}}=3-2\frac{2}{3}\)
\(\Leftrightarrow\frac{1}{2}.\frac{x}{x+1}=\frac{1}{3}\)
\(\Leftrightarrow\frac{x}{x+1}=\frac{2}{3}\)
\(\Leftrightarrow3x=2\left(x+1\right)\)
\(\Leftrightarrow3x-2x=2\)
\(\Leftrightarrow x=2\)
Vậy \(S=\left\{2\right\}\)
Tìm x biết:
1) \(\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}=\frac{x+1}{5}+\frac{x+1}{6}\)
2) \(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}\)
Tìm số nguyên x biết: a) \(-4\frac{3}{5}.2\frac{4}{23}\le x\le-2\frac{3}{5}:1\frac{6}{15}\)
b) \(-4\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{6}\right)\le x\le-\frac{2}{3}\left(\frac{1}{3}-\frac{1}{2}-\frac{3}{4}\right)\)
Tìm x biết \(\frac{x+2}{327}+\frac{x+3}{326}+\frac{x+4}{325}+\frac{x+5}{324}+\frac{x+349}{5}=0\)
CMR:\(\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}< 1\)
\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{100}}>10\)
Tính \(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{20}\left(1+2+3+...+20\right)\)
CMR: \(\frac{1}{2^2}-\frac{1}{2^4}+\frac{1}{2^6}-...+\frac{1}{2^{2002}}-\frac{1}{2^{2004}}< 0,2\)
tìm x biết:
\(|x-\frac{1}{3}|=|\left(-3,2\right)+\frac{2}{5}|\)
\(\frac{x-1}{2011}+\frac{x-2}{2010}-\frac{x-3}{2009}=\frac{x-4}{2008}\)
Tìm x,y biết : |x-y|=1\(\frac{1}{2}\)
a)\(\frac{-1}{2}+\left(x-3\right):\frac{-1}{2}=-1\frac{2}{3}\)
c)\(\left(\frac{1}{3}-x\right)^2=\frac{1}{4}\)
b)\(2,25+\frac{3}{2}:\left(x-5\right)=2\frac{1}{2}\)
d)\(\frac{3}{2}+\frac{x-1}{3}=1\)
e)\(\frac{-6}{8}+\frac{x}{12}=\frac{5}{6}\)
g)\(\frac{1}{2}-\frac{1}{3}\left(x-2\right)=\frac{-2}{3}\)
h)\(\frac{5}{2}\left(x+1\right)-\frac{1}{2}=3\frac{1}{2}\)
k)\(\frac{x}{3}-\frac{1}{2}=-2\left(x+1\right)+3\)
Tìm số nguyên x biết \(-4\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{6}\right)\le x\le-\frac{2}{3}.\left(\frac{1}{3}-\frac{1}{2}-\frac{3}{4}\right)\)
Bài 1 : Tìm x biết :
a, \(\left|\frac{3}{2}x+\frac{1}{2}\right|=\left|4x-1\right|\)
b, \(\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)
c,\(\left|\frac{7}{5}x+\frac{2}{3}\right|=\left|\frac{4}{3}x-\frac{1}{4}\right|\)
Bài 2 : Tìm x biết :
a, | 2x - 5 | = x +1
b, | 3x - 2 | -1 = x
c, | 3x - 7 | = 2x + 1
d, | 2x-1 | +1 = x
Tìm x biết : \(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2004}\right)x=\frac{2013}{1}+\frac{2012}{2}+...+\frac{2}{2012}+\frac{1}{2013}\)
1. So sánh:
a. 1 và \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{50}}\)
b. \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^{100}}\)với \(\frac{1}{2}\)
c. \(\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^6}+.....\frac{1}{4^{1000}}\)với \(\frac{1}{3}\)
2. Tìm x, biết:
a.\(\left(\frac{2}{5}-x\right):1\frac{1}{3}+\frac{1}{2}=-4\)
b.\(3-\frac{1-\frac{1}{2}}{1+\frac{1}{x}}=2\frac{2}{3}\)
c.\(4^x+4^{x+3}=4160\)
d.\(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)
e.\(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{24}=3\)
g.\(\frac{x-1}{65}+\frac{x-3}{63}+=\frac{x-5}{61}+\frac{x-7}{59}\)
