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Binomial Theorem

Source: 2002 National High School Mathematics League, Exam One, Problem 8

March 16, 2020
algebrabinomial theoremarithmetic sequencecalculusintegration

Problem Statement

Consider the expanded form of (x+12x4)n\left(x+\frac{1}{2\sqrt[4]{x}}\right)^n, put all items in number (from high power to low power). If the coefficients of the first three items are arithmetic sequence, then the number of items with an integral power is________.
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