$lim n \to \infty \frac{^{n} P_{n}}{^{n + 1} P_{n} -^{n} P_{n}} =$

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Solution

$lim n \to \infty \frac{^{n} P_{n}}{^{n + 1} P_{n} -^{n} P_{n}}$
$= lim n \to \infty \frac{n!}{(n + 1)! - n!}$
$= lim n \to \infty \frac{1}{n} = 0$

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lim n \to \infty \frac{^{n} P_{n}}{^{n + 1} P_{n + 1} -^{n} P_{n}} =

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n =

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n

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