The coefficient of $x^9$ in the expansion of $(1 + x)(1 + x^2)(1 + x^3)\cdots(1 + x^{100})$ is:
Step-by-Step Solution
Key Concept: Each factor contributes either 1 or its own power of $x$ to a term, so the coefficient of $x^9$ equals the number of ways of writing 9 as a sum of distinct positive integers (each at most 100) — i.e., count the partitions of 9 into distinct parts.
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Correct Answer: (1)