\[ { }^{1} P_{1}+2 \cdot{ }^{2} P_{2}+3 \cdot{ }^{3} P_{3}+\ldots . .+n \cdot{ }^{\mathrm{n}} P_...

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\[
{ }^{1} P_{1}+2 \cdot{ }^{2} P_{2}+3 \cdot{ }^{3} P_{3}+\ldots . .+n \cdot{ }^{\mathrm{n}} P_{\mathrm{n}}=
\]
(a) \( { }^{\mathrm{n}+1} P_{\mathrm{n}+1} \)
(b) \( { }^{\mathrm{n}+1} P_{\mathrm{n}+1}-1 \)
(c) \( { }^{\mathrm{n}+1} P_{\mathrm{n}+1}-2 \)
(d) \( { }^{\mathrm{n}+1} P_{\mathrm{n}} \)
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