prove the following inequality using am gm hm or weirstrass etc

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For $a_0,a_1,a_2,......,a_n \in R, \,\, a_0<a_1<a_2<....<a_n$ show that $$ \frac n{a_1-a_0}+\frac {n-1}{a_2-a_1}+....+\frac 1{a_n-a_{n-1}} \ge \sum_{k=1}^n \frac {k^2}{a_k} $$ i recently studied inequalities am gm hm , tchebychev, weirstrass, cauchy schwarz. i am trying to solve some questions i don't know how to start on this one can someone please help me on this.