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What is the remainder when 1!+2!+3!+…+29!+30!1! + 2! + 3! + \ldots + 29! + 30!1!+2!+3!+…+29!+30! is divided by 100100100?
Details and assumptions
The notation n! n!n! (read as nnn factorial) refers to multiplying all the positive integers from 111 to nnn. For example, 8!=8×7×6×5×4×3×2×1 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 18!=8×7×6×5×4×3×2×1.
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