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Bosnia and Herzegovina TST 2003 Day 1 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 2003

September 18, 2018

Inequalityalgebrapositive integer

Problem Statement

Prove that for every positive integer

n

holds:

(n-1)^n+2n^n \leq (n+1)^{n} \leq 2(n-1)^n+2n^{n}