\(\left(1-\frac{2}{5}\right).\left(1-\frac{2}{7}\right)...\left(1-\frac{2}{2013}\right).\left(1-\frac{2}{2015}\right)\)
\(=\frac{3}{5}.\frac{5}{7}...\frac{2011}{2013}.\frac{2013}{2015}\)
\(=\frac{3.5...2011.2013}{5.7...2013.2015}\)
\(=\frac{3}{2015}\)
\(\left(1-\frac{2}{5}\right).\left(1-\frac{2}{7}\right)....\left(1-\frac{2}{2013}\right).\left(1-\frac{2}{2015}\right)\)
\(=\frac{3}{5}.\frac{5}{7}........\frac{2011}{2013}.\frac{2013}{2015}\)
\(=\frac{3}{2015}\)
\(\left(1-\frac{2}{5}\right).\left(1-\frac{2}{7}\right)...\left(1-\frac{2}{2015}\right)\)
\(=\frac{3}{5}.\frac{5}{7}...\frac{2013}{2015}\)
\(=\frac{3.5.7...2013}{5.7.9...2015}\)
\(=\frac{3}{2015}\)
\(\left(1-\frac{2}{5}\right).\left(1-\frac{2}{7}\right)......\left(1-\frac{2}{2013}\right).\left(1-\frac{2}{2015}\right)\)
\(\Rightarrow\frac{3}{5}.\frac{5}{7}......\frac{2011}{2013}.\frac{2013}{2015}\)
\(\Rightarrow\frac{3.5......2011.2013}{5.7......2013.2015}\)
Đơn giản hết sẽ là:
\(\frac{3}{2015}\)
