Q.

The coefficient of x4 in the expansion of 1+x+x2+x36in powers of x is .......

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answer is 120.

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Detailed Solution

The coefficient of x4 in the expansion of 1+x+x2+x36= coefficient of x4 in 1−x41−x6= coefticient of x4 in 1−6x4(1−x)−6= coefficient of x4 in 1−6x41+6C1x+7C2x2+…=9C4−6=9×8×7×64×3×2−6=126−6=120
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