3 Sean $k \geq 2, 1 < n_1 < n_2 < \ldots < n_k$ enteros positivos, $a,b \in \mathbb{Z}^+$ que satisfacen \[ \prod^k_{i=1} \left( 1 - \frac{1}{n_i} \right) \leq \frac{a}{b} < \prod^{k-1}_{i=1} \left( 1 - \frac{1}{n_i} \right) \] Demuestre que: \[ \prod^k_{i=1} n_i \geq (4 \cdot a)^{2^k - 1}. \]