\(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+\frac{2}{11\times13}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\)
\(=\frac{1}{3}-\frac{1}{13}\)
\(=\frac{13}{39}-\frac{3}{39}=\frac{13-3}{39}=\frac{10}{39}\)
\(\frac{2}{3x5}\)+ \(\frac{2}{5x7}\)+ \(\frac{2}{7x9}\)+ \(\frac{2}{9x11}\)+ \(\frac{2}{11x13}\)
= \(\frac{1}{3}\)- \(\frac{1}{5}\)+ \(\frac{1}{5}\)- \(\frac{1}{7}\)+ ... + \(\frac{1}{11}\)- \(\frac{1}{13}\)
= \(\frac{1}{3}\)- \(\frac{1}{13}\)
= \(\frac{10}{39}\)
\(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\)\(+\frac{2}{11\times13}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)
\(=\frac{1}{3}-\frac{1}{13}\)
\(=\frac{10}{39}\)
Nó là quy luật nhé bạn