Problem

Source: China TST 2002 Quiz

Tags: algebra unsolved, algebra



Given a positive integer $ n$, for all positive integers $ a_1, a_2, \cdots, a_n$ that satisfy $ a_1 = 1$, $ a_{i + 1} \leq a_i + 1$, find $ \displaystyle \sum_{i = 1}^{n} a_1a_2 \cdots a_i$.