How many digits has the sum of the first factorials?

(a) How many digits has the number s defined below? s = 0! + 1! + 2! + 3! + 4! + ... + (n-1)! + n! (b) define: ₙ ∑ i! = s(n) ⁱ⁼¹ prove that s(n) ≡ 4 (mod 10) for any integer n > 3