Ta có \(N = \frac{1}{2}\left( {\frac{2}{{1.2.3}} + \frac{2}{{2.3.4}} + \frac{2}{{3.4.5}} + ... + \frac{2}{{n.(n + 1)(n + 2)}}} \right)\)
\( = \frac{1}{2}\left( {\frac{1}{{1.2}} - \frac{1}{{2.3}} + \frac{1}{{2.3}} - \frac{1}{{3.4}} + \frac{1}{{3.4}} - \frac{1}{{4.5}} + ... + \frac{1}{{n(n + 1)}} - \frac{1}{{(n + 1)(n + 2)}}} \right)\)
\( = \frac{1}{2}\left( {\frac{1}{2} - \frac{1}{{(n + 1)(n + 2)}}} \right)\)
