Question 16
(ISR 1) The set $\{a_0,a_1,\ldots,a_n\}$ of real numbers satisfies the following conditions:
(i) $a_0=a_n=0$;
(ii) for $1\le k\le n-1$,
$$a_k=c+\sum_{i=k}^{n-1}a_{i-k}(a_i+a_{i+1}).$$
Prove that $c\le\frac1{4n}$.
(i) $a_0=a_n=0$;
(ii) for $1\le k\le n-1$,
$$a_k=c+\sum_{i=k}^{n-1}a_{i-k}(a_i+a_{i+1}).$$
Prove that $c\le\frac1{4n}$.