Summation of factorials modulo ten I have read that$$\sum\limits_{i=1}^n i!\equiv3\;(\text{mod }10),\quad n> 3.$$
Why is the sum constant, and why is it $3$?

Think about what you are summing:
$$1+2+6+24+120+720+\dots = 33 + 120 + 720 + \dots$$
Taking mod $10$ of the sum, you can see that $33$ gives $3$, can you see that all other sumands are divisible by $10$?
