The sequence a1,a2,...,a2019 satisfies the following condition.
a1=1,an+1=2019an+1
Now let x1,x2,...,x2019 real numbers such that x1=a2019,x2019=a1 (The others are arbitary.)
Prove that ∑k=12018(xk+1−2019xk−1)2≥∑k=12018(a2019−k−2019a2020−k−1)2