Let \( P_{m} \) stand for \( { }^{m} P_{m} \). Then the expression ...

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Let \( P_{m} \) stand for \( { }^{m} P_{m} \). Then the expression \( 1 \cdot P_{1}+2 \cdot P_{2}+3 \cdot P_{3}+\cdots \ldots+n \cdot P_{n}= \)
(1) \( (n+1) !-1 \)
(2) \( (n+1) !+1 \)
(3) \( (n+1) \) !
(4) none
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