Question

\(\left(1\dfrac{2}{3}\right)\left(1\dfrac{2}{5}\right)\left(1\dfrac{2}{7}\right).......\left(1\dfrac{2}{2011}\right)\left(1\dfrac{2}{2013}\right)\)

Answer 1

Ta có : \(\left(1\dfrac{2}{3}\right)\left(1\dfrac{2}{5}\right).....\left(1\dfrac{2}{2011}\right)\left(1\dfrac{2}{2013}\right)\)

\(=\dfrac{5}{3}.\dfrac{7}{5}....\dfrac{2013}{2011}.\dfrac{2015}{2013}=\dfrac{2015}{3}\)
 

Answer 2

\(\left(1\dfrac{2}{3}\right)\left(1\dfrac{2}{5}\right)\left(1\dfrac{2}{7}\right)...\left(1\dfrac{2}{2011}\right)\left(1\dfrac{2}{2013}\right)\)

\(=\dfrac{5}{3}.\dfrac{7}{5}.\dfrac{9}{7}.....\dfrac{2013}{2011}.\dfrac{2015}{2013}\)

\(=\dfrac{2015}{3}\)

Answer 3

\(\left(1\dfrac{2}{3}\right)\left(1\dfrac{2}{5}\right)\left(1\dfrac{2}{7}\right)...\left(1\dfrac{2}{2013}\right)\)

\(=\dfrac{5}{3}.\dfrac{7}{5}.\dfrac{9}{7}...\dfrac{2015}{2013}=\dfrac{2015}{3}\)

Answer 4

\(\left(1\dfrac{2}{3}\right).\left(1\dfrac{2}{5}\right).\left(1\dfrac{2}{7}\right).....\left(1\dfrac{2}{2011}\right).\left(1\dfrac{2}{2013}\right)\) 

\(=\dfrac{5}{3}.\dfrac{7}{5}.\dfrac{9}{7}.....\dfrac{2013}{2011}.\dfrac{2015}{2013}\) 

\(=\dfrac{5.7.9.....2013.2015}{3.5.7.....2011.2013}\) 

\(=\dfrac{2015}{3}\)