\(C=\left(1+\frac{2}{3}\right)\cdot\left(1+\frac{2}{5}\right)\cdot\left(1+\frac{2}{7}\right)\cdot\cdot\cdot\cdot\cdot\left(1+\frac{2}{2009}\right)\cdot\left(1+\frac{2}{2011}\right)\)
\(C=\frac{5}{3}\cdot\frac{7}{5}\cdot\frac{9}{7}\cdot\cdot\cdot\cdot\cdot\frac{2011}{2009}\cdot\frac{2013}{2011}\)
\(C=\frac{5\cdot7\cdot9\cdot\cdot\cdot\cdot\cdot2011\cdot2013}{3\cdot5\cdot7\cdot\cdot\cdot\cdot\cdot2009\cdot2011}\)
\(C=\frac{2013}{3}\)
đề bài của bài là tính
ai nhanh mk k cho
\(C=\left(1+\frac{2}{3}\right).\left(1+\frac{2}{5}\right).....\left(1+\frac{2}{2009}\right).\left(1+\frac{2}{2011}\right)\)
\(C=1\left(\frac{2}{3}+\frac{2}{5}+...+\frac{2}{2009}+\frac{2}{2011}\right)\)
\(\frac{1}{2}C=\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2009}+\frac{1}{2011}\)
\(\frac{1}{2}C=\frac{1}{3+5+...+2011}\)
\(\frac{1}{2}C=\frac{1}{1012035}\)
\(\Rightarrow C=\frac{1}{1012035}:\frac{1}{2}=\frac{2}{1012035}\)
