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Đáp án:
$A = - \frac{197}{199}$
$B = \frac{133}{195}$
Giải thích các bước giải:
$A = \frac{1}{199} - \frac{1}{199.198} - ... - \frac{1}{3.2} - \frac{1}{2.1}$
$= \frac{1}{199} - (\frac{1}{198} - \frac{1}{199}) - ... - (\frac{1}{2} - \frac{1}{3}) - (1 - \frac{1}{2})$
$= \frac{1}{199} + \frac{1}{199} - \frac{1}{198} - ... + \frac{1}{3} - \frac{1}{2} + \frac{1}{2} - 1$
$= \frac{2}{199} - 1$
$= - \frac{197}{199}$
$B = 1- \frac{2}{3.5} - \frac{2}{5.7} - ... - \frac{2}{63.65}$
$= 1 - (\frac{1}{3} - \frac{1}{5}) - (\frac{1}{5} - \frac{1}{7}) - ... - (\frac{1}{63} - \frac{1}{65})$
$= 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{5} + \frac{1}{7} - ... - \frac{1}{63} + \frac{1}{65}$
$= 1 - \frac{1}{3} + \frac{1}{65}$
$= \frac{195}{195} - \frac{65}{195} + \frac{3}{195}$
$= \frac{133}{195}$