# Tag Archives: factorials

## Sum of the first factorials a perfect power?

Consider the following sum: $$F(n) = 1! + 2! + 3! + \cdots + n!$$ Can this sum ever be a perfect power? A perfect power here is defined as $x^n$ for some natural number $x$ and some natural number $n\geq 2$. Some observations immediately come to mind: $F(1) = 1$, and that's trivially a […]