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Q.The coefficient of xnx^{n} in the expansion of 1(1−x)(1−2x)(1−3x)(1−4x)\dfrac{1}{(1-x)(1-2x)(1-3x)(1-4x)} is

a
1+2n+3n+4n1 + 2^n + 3^n + 4^n
b
4n+2−3⋅3n+1+3⋅2n+1−16\dfrac{4^{n+2} - 3 \cdot 3^{n+1} + 3 \cdot 2^{n+1} - 1}{6}
c
4n+3−3n+3+2n+3−16\dfrac{4^{n+3} - 3^{n+3} + 2^{n+3} - 1}{6}
d
4n+1−3⋅3n+3⋅2n−16\dfrac{4^{n+1} - 3 \cdot 3^n + 3 \cdot 2^n - 1}{6}

Correct Answer: Option C

The correct solution involves applying the fundamental concept to derive the final value step by step...

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