The sum of \( (x+2)^{n-1}+(x+2)^{n-2}(x+1)+(x+2)^{n-3}(x+1)^{2} \) \( +\ldots+(x+1)^{n-1} \) is ...

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The sum of \( (x+2)^{n-1}+(x+2)^{n-2}(x+1)+(x+2)^{n-3}(x+1)^{2} \) \( +\ldots+(x+1)^{n-1} \) is equal to
(A) \( (x+2)^{n-2}-(x+1)^{n} \)
(B) \( (x+2)^{n}-(x+1)^{n} \)
(C) \( (x+2)^{n-1}-(x+1)^{n-1} \)
(D) None of these
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