Let and for all

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Let a=31/124+1a = 3^{1/124} + 1 and for all n≥3n \ge 3, let f(n)=nC0an−1−nC1an−2+nC2an−3+⋯+(−1)n−1nCn−1⋅a0.\text{let } f(n) = {}^n C_0 a^{n-1} - {}^n C_1 a^{n-2} + {}^n C_2 a^{n-3} + \dots + (-1)^{n-1} {}^n C_{n-1} \cdot a^0. If the value of f(2016)+f(2017)=3Kf(2016) + f(2017) = 3^K, the value of KK is (1) 6 (2) 8 (3) 9 (4) 10

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