Đáp án:
\(A = \frac{{673}}{{(x + 1)(x + 2020)}}\)
Giải thích các bước giải:
\(\begin{array}{l}
A = \frac{1}{{(x + 1)(x + 4)}} + \frac{1}{{(x + 4)(x + 7)}} + \frac{1}{{(x + 7)(x + 10)}} + ... + \frac{1}{{(x + 2017)(x + 2020)}}\\
3A = \frac{3}{{(x + 1)(x + 4)}} + \frac{3}{{(x + 4)(x + 7)}} + \frac{3}{{(x + 7)(x + 10)}} + ... + \frac{3}{{(x + 2017)(x + 2020)}}\\
= \frac{1}{{x + 1}} - \frac{1}{{x + 4}} + \frac{1}{{x + 4}} - \frac{1}{{x + 7}} + \frac{1}{{x + 7}} - \frac{1}{{x + 10}} + ... + \frac{1}{{x + 2017}} - \frac{1}{{x + 2020}}\\
= \frac{1}{{x + 1}} - \frac{1}{{x + 2020}} = \frac{{x + 2020 - x - 1}}{{(x + 1)(x + 2020)}} = \frac{{2019}}{{(x + 1)(x + 2020)}}\\
A = \frac{{673}}{{(x + 1)(x + 2020)}}
\end{array}\)
