(Solution) - Show that the coefficient pd n of xn in the -(2025 Original AI-Free Solution)

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Show that the coefficient pd (n) of xn in the formal power series expansion of (1 + x) (1 + x2) (1 + x3) ··· equals the number of partitions of n into distinct parts, that is, the number of ways to write n as the sum of positive integers, where the order does not matter but no repetitions are allowed.