Đáp án:
Giải thích các bước giải:
$\color {cream } {N = \frac{1}{5 \times 10} + \frac{1}{10 \times 15} + \frac{1}{15 \times 20} + ... + \frac{1}{2005 \times 2010} \\\Leftrightarrow 5N = \frac{5}{5 \times 10} + \frac{5}{10 \times 15} + \frac{5}{15 \times 20} + ... + \frac{5}{2005 \times 2010} \\\Leftrightarrow 5N = \frac{1}{5} - \frac{1}{10} + \frac{1}{10} - \frac{1}{20} + \frac{1}{20} - \frac{1}{25} + \frac{1}{2005} - \frac{1}{2010} \\\Leftrightarrow 5N = \frac{1}{5} - \frac{1}{2010} \\\Leftrightarrow N = \frac{401}{10050} } $