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Factorial pattern

$$1\times1!=2!-1$$ $$1\times1!+2\times2!=3!-1$$ $$1\times1!+2\times2!+3\times3!=4!-1$$
Does this pattern continue?

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If you enjoyed this puzzle, check out Sunday Afternoon Maths LVIII,
puzzles about factorials, or a random puzzle.

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