Đáp án:
$S=\frac{31}{47}$
Giải thích các bước giải:
$S=\frac{2}{1.4}+\frac{2}{4.7}+...+\frac{2}{91.94}\\
=2.\left ( \frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{91.94} \right )\\
=2.\frac{1}{3}.\left ( \frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{91.94} \right )\\
=2.\frac{1}{3}.\left ( \frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{91}-\frac{1}{94} \right )\\
=\frac{2}{3}.\left ( 1-\frac{1}{94} \right )\\
=\frac{2}{3}.\left ( \frac{94}{94}-\frac{1}{94} \right )\\
=\frac{2}{3}.\frac{93}{94}\\
=\frac{31}{47}$
