The coefficient of \( x^{n} \) in the expansion of \( \dfrac{1}{(1-x)(1-2x)(1-3x)} \) is ;

A \( \dfrac{1}{2}(2^{n+2}-3^{n+3}+1) \)

B \( \dfrac{1}{2}(3^{n+2}-2^{n+3}+1) \)

C \( \dfrac{1}{2}(2^{n+3}-3^{n+2}+1) \)

D \( none\ of\ these \)

Solution

Correct Answer: Option B

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