Đáp án:
Giải thích các bước giải:
a, $\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+50}$
$=\frac{1}{\frac{2.(2+1)}{2}} + \frac{1}{\frac{3.(3+1)}{2}} + \frac{1}{\frac{4.(4+1)}{2}} + ... + \frac{1}{\frac{50.(50+1)}{2}}$
$= \frac{2}{2.3} + \frac{2}{3.4} + \frac{2}{4.5} + ... + \frac{2}{50.51} $
$= 2. ( \frac{1}{2.3} + \frac{1}{3.4} + \frac{1}{4.5} + ... + \frac{1}{50.51} ) $
$= 2. ( \frac{1}{2} - \frac{1}{3} + \frac{1}{3} -\frac{1}{4}+ \frac{1}{4} - \frac{1}{5} + ... + \frac{1}{50} - \frac{1}{51} ) $
$= 2. ( \frac{1}{2} - \frac{1}{51} ) $
$= 2. \frac{49}{102} $
$= \frac{49}{51} $
b, $ \frac{1}{1.4} + \frac{1}{2.6} + \frac{1}{3.8}$