Atrisinājums

Nē, \(2019~\mathrm{-ais}\) loceklis var nebūt naturāls skaitlis, piemēram, ja \(b_{1}=1 \in \mathbb{N}\) un \(q=\sqrt[3]{2}\), tad

• \(b_{10}=b_{1} \cdot q^{9}=(\sqrt[3]{2})^{9}=2^{3}=8 \in \mathbb{N}\),
• \(b_{2020}=b_{1} \cdot q^{2019}=(\sqrt[3]{2})^{2019}=2^{673} \in \mathbb{N}\),
• \(b_{2019}=b_{1} \cdot q^{2018}=(\sqrt[3]{2})^{2016} \cdot(\sqrt[3]{2})^{2}=2^{672} \cdot \sqrt[3]{4}\), kas nav naturāls skaitlis.