Tính 2/5x9 2/9x13 ... 2/81x85

Lời giải:

\(\begin{array}{l}A = \frac{2}{{1.5}} + \frac{2}{{5.9}} + \frac{2}{{9.13}} + ... + \frac{2}{{81.85}}\\2A = \frac{4}{{1.5}} + \frac{4}{{5.9}} + \frac{4}{{9.13}} + ... + \frac{4}{{81.85}}\\2A = 1 - \frac{1}{5} + \frac{1}{5} - \frac{1}{9} + ... + \frac{1}{{81}} - \frac{1}{{85}}\\2A = 1 - \frac{1}{{85}}\\A = \frac{{84}}{{85}}:2 = \frac{{42}}{{85}}\end{array}\)