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min f(n+2)/f(n), if f(n) =1^n + 2^{n-1} + 3^{n-2}+ 4^{n-3}+... + (n-1)^2 + n^1

Source: Singapore Senior Math Olympiad 2001 2nd Round p2 SMO

April 4, 2020
inequalitiesminalgebra

Problem Statement

Let nn be a positive integer, and let f(n)=1n+2n−1+3n−2+4n−3+...+(n−1)2+n1f(n) =1^n + 2^{n-1} + 3^{n-2}+ 4^{n-3}+... + (n-1)^2 + n^1 Find the smallest possible value of f(n+2)f(n)\frac{f(n+2)}{f(n)} .Justify your answer.
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