Let (an)n≥0 be a sequence of positive numbers that satisfy the relations ai−1ai+1≤a2i for all i∈N. For any integer n>1, prove the inequality a0+…+ann+1⋅a1+…+an−1n−1≥a0+…+an−1n⋅a1+…+ann.
Source: Moldova 2000 Grade 11 P6
Tags: Inequality, inequalities
Let (an)n≥0 be a sequence of positive numbers that satisfy the relations ai−1ai+1≤a2i for all i∈N. For any integer n>1, prove the inequality a0+…+ann+1⋅a1+…+an−1n−1≥a0+…+an−1n⋅a1+…+ann.