St.Petersburg 1999 :Let $x_0>x_1>\dots >x_n$ be real numbers. Prove that $$ x_0+\frac{1}{x_0-x_1}+\frac{1}{x_1-x_2}+\dots+\frac{1}{x_{n-1}-x_n}\ge x_n+2n $$ I tried Titu's inequality. So we get $$ x_0+\frac{1}{x_0-x_1}+\frac{1}{x_1-x_2}+\dots+\frac{1}{x_{n-1}-x_n}= x_0+\frac{1^2}{x_0-x_1}+\frac...