$\frac{1}{1.3.5}$ + $\frac{1}{3.5.7}$ + $\frac{1}{5.7.9}$+...+ $\frac{1}{2011.2013.2015}$
= $\frac{5-1}{1.3.5.4}$ + $\frac{7-3}{3.5.7.4}$ + $\frac{9-5}{5.7.9.4}$+...+ $\frac{2015-2011}{2011.2013.2015.4}$
=$\frac{1}{4}$.($\frac{5-1}{1.3.5}$ + $\frac{7-3}{3.5.7}$ + $\frac{9-5}{5.7.9}$+...+ $\frac{2015-2011}{2011.2013.2015}$)
=$\frac{1}{4}$.($\frac{5}{1.3.5}$ - $\frac{1}{1.3.5}$+ $\frac{7}{3.5.7}$ -$\frac{3}{3.5.7}$ + $\frac{9}{5.7.9}$ - $\frac{5}{5.7.9}$+...+ $\frac{2015}{2011.2013.2015}$ - $\frac{2011}{2011.2013.2015}$)
=$\frac{1}{4}$.($\frac{1}{3}$ - $\frac{1}{3.5}$+ $\frac{1}{3.5}$ -$\frac{1}{5.7}$ + $\frac{1}{5.7}$ - $\frac{1}{7.9}$+...+ $\frac{1}{2011.2013}$ - $\frac{1}{2013.2015}$)
=$\frac{1}{4}$.($\frac{1}{3}$ - $\frac{1}{2013.2015}$)
=$\frac{1}{4}$.$\frac{4056194}{12168585}$
=0,083333312
(Bạn chuyển sang phân số và tối giản hộ mình nha).
