MathDB

Sequence of real numbers

a_0,a_1,\dots,a_{1389}

are called concave if for each

0<i<1389

a_i\geq\frac{a_{i-1}+a_{i+1}}2

. Find the largest

c

such that for every concave sequence of non-negative real numbers:

\sum_{i=0}^{1389}ia_i^2\geq c\sum_{i=0}^{1389}a_i^2

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