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\(\frac{x}{2}-\frac{1}{x}=\frac{1}{12}\Rightarrow\frac{x^2}{2}-\frac{x}{x}=\frac{1}{6}\)
\(\Rightarrow\frac{x^2}{2}-1=\frac{1}{6}\Rightarrow\frac{x^2}{2}=\frac{1}{6}+1=\frac{7}{6}\)
\(\Rightarrow x^2=\frac{7}{6}.2=\frac{7}{3}\)
\(\Rightarrow x=1.5275252317\)
\(\text{Mình nhầm :}\)
\(\frac{x}{2}-\frac{1}{x}=\frac{1}{12}\Rightarrow\frac{x^2}{2}-\frac{x}{x}=\frac{1}{6}\)
\(\Rightarrow\frac{x^2}{2}-1=\frac{1}{6}\Rightarrow\frac{x^2}{2}=\frac{1}{6}+1=\frac{7}{6}\)
\(\Rightarrow x^2=\frac{7}{6}.2=\frac{7}{12}\)
\(\Rightarrow x = 0.76376261583\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{x\left(x+1\right) }=\frac{2015}{4034}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2015}{4034}\)
\(x=2016\)
\(S^{2020}\)và\(S^{2021}\)?Thế này sai mất thui.
Vì \(2020< 2021\)nên\(S^{2020}< S^{2021}\).
\(3A=3\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\right)\)
\(3A=1+\frac{1}{3}+...+\frac{1}{3^7}\)
\(3A-A=\left(1+\frac{1}{3}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\right)\)
\(2A=1-\frac{1}{3^8}\)
\(A=\frac{6560}{6561}:2\)
\(A=\frac{3280}{6561}\)
a ) \(\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)
\(=\frac{4}{20}+\frac{8}{21}+\frac{2}{5}-\frac{3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)
\(=\left(\frac{4}{20}+\frac{3}{20}\right)+\left(\frac{8}{21}+\frac{2}{21}-\frac{10}{21}\right)+\left(\frac{2}{5}-\frac{3}{5}\right)\)
\(=\frac{7}{20}+0+\frac{-1}{5}=\frac{7-4}{20}=\frac{3}{20}\)
b ) \(\frac{42}{46}+\frac{250}{186}+\frac{-2121}{2323}+\frac{-125125}{143143}\)
\(=\frac{21}{23}+\frac{-21}{23}+\frac{-125}{143}\)
\(=0+\frac{-125}{143}=-\frac{125}{143}\)
bài 2
a \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2003.2004}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2003}-\frac{1}{2004}\)
=\(1-\frac{1}{2004}=\frac{2003}{2004}\)
Ta có : \(\left(1\frac{1}{15}\right).\left(1\frac{1}{16}\right).....\left(1\frac{1}{2020}\right)=\frac{16}{15}.\frac{17}{16}....\frac{2021}{2020}=\frac{16.17....2021}{15.16....2020}=\frac{2021}{15}\)
thank cậu nhiều nhiều