GATE 2016 CS – Question 36
The coefficient of $x^{12}$ in $(x^3 + x^4 + x^5 + x^6 + \cdots)^3$ is ________.
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Correct answer: 10
Explanation
Factor out $x^3$ from each bracket: $(x^3 + x^4 + \cdots)^3 = x^9 (1 + x + x^2 + \cdots)^3 = x^9 (1 - x)^{-3}$. The coefficient of $x^{12}$ is the coefficient of $x^3$ in $(1 - x)^{-3}$, which is $\binom{3 + 2}{2} = 10$.