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min term of a_n = 1/4 n^4 - 10n^2(n - 1)

Source: Spanish Mathematical Olympiad 1973 P1

December 5, 2022
Sequencealgebra

Problem Statement

Given the sequence (an)(a_n), in which an=14n410n2(n1)a_n =\frac14 n^4 - 10n^2(n - 1), with n=0,1,2,...n = 0, 1, 2,... Determine the smallest term of the sequence.