Using \( \lim _{x \rightarrow a}\left(\frac{x^{n}-a^{n}}{x-a}\right)=n a^{n-1} \), answer the fo....

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Using \( \lim _{x \rightarrow a}\left(\frac{x^{n}-a^{n}}{x-a}\right)=n a^{n-1} \), answer the following
\( \mathrm{P} \)
questions.

If \( n \) is a positive integer then
\[
\lim _{x \rightarrow 1}\left(\frac{x^{n+1}-(n+1) x+n}{(x-1)^{2}}\right)=
\]
(1) \( \frac{n}{2} \)
(2) \( \frac{n+1}{2} \)
(3) \( \frac{n(n+1)}{2} \)
(4) \( \frac{n(n+1)(2 n-1)}{2} \)


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