Let \( S_{n}(1 \leq n \leq 9) \) denotes the sum of \( n \) terms o...

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Let \( S_{n}(1 \leq n \leq 9) \) denotes the sum of \( n \) terms of the series
\( \mathrm{P} \) \( 1+22+333+\ldots+\underbrace{999 \ldots 9}_{9 \text { times }} \), then for \( 2 \leq n \leq 9 \)

W.
(a) \( S_{n}-S_{n-1}=\frac{1}{9}\left(10^{n}-n^{2}+n\right) \)
(b) \( S_{n}=\frac{1}{9}\left(10^{n}-n^{2}+2 n-2\right) \)
(c) \( 9\left(S_{n}-S_{n-1}\right)=n\left(10^{n}-1\right) \)
(d) None of the above
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