Question 4
(SWE) Let $a_1,a_2,\ldots,a_n,\ldots$ be a sequence of real numbers such that $0\le a_n\le1$ and $a_n-2a_{n+1}+a_{n+2}\ge0$ for $n=1,2,3,\ldots$. Prove that
$$0\le(n+1)(a_n-a_{n+1})\le2$$
for $n=1,2,3,\ldots$.
$$0\le(n+1)(a_n-a_{n+1})\le2$$
for $n=1,2,3,\ldots$.