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a/
\(1\frac{1}{2}x1\frac{1}{3}x1\frac{1}{4}x1\frac{1}{5}x1\frac{1}{6}=\frac{3}{2}x\frac{4}{3}x\frac{5}{4}x\frac{6}{5}x\frac{7}{6}=\frac{7}{2}=3\frac{1}{2}\)
b/
x=0; y=5
\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{x\cdot(x+2)}=\frac{100}{101}\)
\(\Rightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{100}{101}\)
\(\Rightarrow1-\frac{1}{x+2}=\frac{100}{101}\)
\(\Rightarrow\frac{1}{x+2}=\frac{1}{101}\)
\(\Leftrightarrow x+2=101\Leftrightarrow x=99\)
Vậy x = 99
\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{2015}\right)\)
\(=\left(\frac{2-1}{2}\right)\left(\frac{3-1}{3}\right)\left(\frac{4-1}{4}\right)....\left(\frac{2015-1}{2015}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{2013}{2014}.\frac{2014}{2015}\)
\(=\frac{1}{2015}\)
a) \(\left(x+\frac{3}{4}\right):5=\frac{5}{6}\)
\(x+\frac{3}{4}=\frac{5}{6}\text{x}5\)
\(x+\frac{3}{4}=\frac{25}{6}\)
\(x=\frac{25}{6}-\frac{3}{4}\)
\(x=\frac{41}{12}\)
b) \(\left(\frac{4}{3}+x\right)\text{x}\frac{1}{11}=\frac{7}{11}\)
\(\frac{4}{3}+x=\frac{7}{11}:\frac{1}{11}\)
\(\frac{4}{3}+x=7\)
\(x=7-\frac{4}{3}\)
\(x=\frac{17}{3}\)
a) \(x+\frac{3}{4}\div5=\frac{5}{6}\)
\(x+\frac{3}{4}=\frac{5}{6}\times5\)
\(x+\frac{3}{4}=\frac{25}{6}\)
\(x=\frac{25}{6}-\frac{3}{4}\)
\(x=\frac{41}{21}\)
b) \(\left(\frac{4}{3}+x\right)\times\frac{1}{11}=\frac{7}{11}\)
\(\frac{4}{3}+x=\frac{7}{11}\div\frac{1}{11}\)
\(\frac{4}{3}+x=7\)
\(x=7-\frac{4}{3}\)
\(x=\frac{17}{3}\)
\(a\cdot\frac{1}{5}+80\%\cdot a=20152015,15\)
\(\Rightarrow a\cdot\frac{1}{5}+\frac{4}{5}\cdot a=20152015,15\)
\(\Rightarrow a\cdot\left(\frac{1}{5}+\frac{4}{5}\right)=20152015,15\)
\(\Rightarrow a\cdot1=20152015,15\Rightarrow a=20152015,15:1=20152015,15\)