\(a_n+a_{n+1}\)
\(=\left(1+2+3+...+n\right)+\left(1+2+3+...+n+1\right)\)
\(=\frac{n\left(n+1\right)}{2}+\frac{\left(n+1\right)\left(n+2\right)}{2}\)
\(=\frac{n^2+n}{2}+\frac{n^2+3n+2}{2}\)
\(=\frac{2n^2+4n+2}{2}\)
\(=n^2+2n+1=\left(n+1\right)^2\) là số chính phương