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Let $x$ be a nonzero number. Which of the following is equal to:
$$\sum_{k=0}^{n-1}(k+1)\binom{n}{k+1}x^{k}$$

A

$(k+1)(1+x)^{n-1}$

B

$n(1+x)^{n-1}$

C

$n(1+x)^n$

D

$(1+x)^n-x^n$

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