Đáp án:

Giải thích các bước giải:

1/1+2+1/1+2+3+1/1+2+3+4+...+1/1+2+3+...+50

=1/2.(2+1/)2+1/3.(3+1)/2+1/4.(4+1)/2+...+1/50.(50+1)/2 

=2/2.3/2/3.4+2/4.5+...+2/50.51

=2.(1/2.3+1/3.4+1/4.5+...+1/50.51)

=2.(1/2−1/3+1/3−1/4+1/4−1/5+...+1/50−1/51)

=2.(1/2−1/51)

=2.49/102

=49/51

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}$