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Binomial Theorem

Source: 2000 National High School Mathematics League, Exam One, Problem 8

March 10, 2020
algebrabinomial theorem

Problem Statement

Define ana_n: the coefficient of then item xx in (3−x)n(3-\sqrt{x})^n, where nn is a positive integer. Then lim⁡n→∞(32a2+33a3+⋯+3nan)=\lim_{n\to\infty}\left(\frac{3^2}{a_2}+\frac{3^3}{a_3}+\cdots+\frac{3^n}{a_n}\right)=________.
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