Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}S = 1 - \frac{1}{{1 \times 2}} + 1 - \frac{1}{{2 \times 3}} + .... + 1 - \frac{1}{{2019 \times 2020}}\\ = \underbrace {\left( {1 + 1 + ... + 1} \right)}_{2019} - \left( {\frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + .... + \frac{1}{{2019.2020}}} \right)\\ = \,\,\,\,\,\,\,\,2019 - \left( {\frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + .... + \frac{1}{{2019}} - \frac{1}{{2020}}} \right)\\ = 2019 - \left( {1 - \frac{1}{{2020}}} \right)\\ = 2019 - \frac{{2019}}{{2020}}\end{array}\)
