n.(n + 1) = 6
n2 + n = 6
n2 + n - 6 = 0
n2 + 3n - 2n - 6 = 0
(n2 + 3n) - (2n + 6) = 0
n . (n + 3) - 2 . (n + 3) = 0
(n + 3) . (n - 2) = 0
\(\Rightarrow\) n + 3 = 0 hoặc n - 2 = 0
Ta có:
\(\left\{{}\begin{matrix}n+3=0\\n-2=0\end{matrix}\right.\) \(\Rightarrow\) \(\left\{{}\begin{matrix}n=-3\\n=2\end{matrix}\right.\)
Mà n \(\in\) N
\(\Rightarrow\) n = 2