## zmudz one year ago Let $$(a_k)$$ be a sequence of integers such that $$a_1 = 1$$ and $$a_{m + n} = a_m + a_n + mn$$ for all positive integers $$m$$ and $$n$$. Find $$a_{12}$$.

Let $$m=1$$, $a_{n+1} = a_n+n+1 \\\implies a_{n+1}-a_n = n+1\\\implies \sum\limits_{n=1}^{11} (a_{n+1}-a_n) = \sum\limits_{n=1}^{11} (n+1)\\$ left side telescopes and right side can be easily evaluated