MathDB

Let

b_1, b_2, \ldots, b_{1989}

be positive real numbers such that the equations x_{r\minus{}1} \minus{} 2x_r \plus{} x_{r\plus{}1} \plus{} b_rx_r \equal{} 0 (1 \leq r \leq 1989) have a solution with x_0 \equal{} x_{1989} \equal{} 0 but not all of

x_1, \ldots, x_{1989}

are equal to zero. Prove that \sum^{1989}_{k\equal{}1} b_k \geq \frac{2}{995}.

Problem Statement