Tính tổng 6/8 + 6/56 + 6/140 + ... + 6/1100 + 6/1400.

* Hướng dẫn giải

$\begin{array}{l}\frac{6}{8}+\frac{6}{56}+\frac{6}{140}+\mathrm{...}+\frac{6}{1100}+\frac{6}{1400}\\ =\frac{2.3}{2.4}+\frac{2.3}{2.28}+\frac{2.3}{2.70}+\mathrm{...}+\frac{2.3}{2.550}+\frac{2.3}{2.700}\\ =\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\mathrm{...}+\frac{3}{550}+\frac{3}{700}\\ =\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\mathrm{...}+\frac{3}{22.25}+\frac{3}{25.28}\\ =1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\mathrm{...}+\frac{1}{22}-\frac{1}{25}+\frac{1}{25}-\frac{1}{28}\\ =1-\frac{1}{28}\\ =\frac{28}{28}-\frac{1}{28}\\ =\frac{27}{28}\end{array}$