Question

For a₁,....,aₙ ∈ R, a₁<a₂< .... <aₙ, show that
n/(a₁-a₀)+(n-1)/(a₂-a₁)+....+1/(aₙ-aₙ₋₁)≥∑ⁿᵤ₌₁u²/aᵤ

Answer 1

This inequality is incorrect. Simple case is n=1, a[0]=-1 and a[1]=1. If we substitute these values, we get 1/2>=1, which is wrong.