Sum cause a Recursion problem

Sum[((-1)^(i + 1)*Binomial[n, i]*(n - i)!)/n!, {i, 1, n}]

This cause a Recursion problem.

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As the comment said, If simplify the formula and then sum it, problem vanished.

((-1)^(i + 1)*Binomial[n, i]*(n - i)!)/n! // FullSimplify // Sum[#, {i, 1, n}] &