Đặt \(C=\left(1+\frac{2}{3}\right)\left(1+\frac{2}{5}\right)\left(1+\frac{2}{7}\right).....\left(1+\frac{2}{2009}\right)\left(1+\frac{2}{2011}\right)\) ta có :
\(C=\left(\frac{3+2}{3}\right)\left(\frac{5+2}{3+2}\right)\left(\frac{7+2}{5+2}\right).....\left(\frac{2009+2}{2007+2}\right)\left(\frac{2011+2}{2009+2}\right)\)
\(C=\frac{\left(3+2\right)\left(5+2\right)\left(7+2\right).....\left(2009+2\right)\left(2011+2\right)}{3\left(3+2\right)\left(5+2\right).....\left(2007+2\right)\left(2009+2\right)}\)
\(C=\frac{2011+2}{3}\)
\(C=\frac{2013}{3}\)
\(C=671\)
Vậy \(C=671\)
Chúc bạn học tốt ~
\(\left(1+\frac{2}{3}\right)\cdot\left(1+\frac{2}{5}\right)\cdot\left(1+\frac{2}{7}\right)...\left(1+\frac{2}{2009}\right)\cdot\left(1+\frac{2}{2011}\right)\)
\(=\frac{5}{3}\cdot\frac{7}{5}\cdot\frac{9}{7}\cdot\cdot\cdot\frac{2011}{2009}\cdot\frac{2013}{2011}\)
\(=\frac{2013}{3}=671\)
