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2.1: Послідовності
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\[\begin{aligned}\left|\frac{x_{i}}{y_{i}}-\frac{L}{M}\right| &=\frac{\left|x_{i} M-y_{i} L\right|}{\left|y_{i} M\right|} \\ &=\frac{\left|x_{i} M-x_{i} y_{i}+x_{i} y_{i}-y_{i} L\right|}{\left|y_{i} M...\[\begin{aligned}\left|\frac{x_{i}}{y_{i}}-\frac{L}{M}\right| &=\frac{\left|x_{i} M-y_{i} L\right|}{\left|y_{i} M\right|} \\ &=\frac{\left|x_{i} M-x_{i} y_{i}+x_{i} y_{i}-y_{i} L\right|}{\left|y_{i} M\right|} \\ & \leq \frac{\left|x_{i}\right|\left|M-y_{i}\right|+\left|y_{i}\right|\left|x_{i}-L\right|}{\left|y_{i} M\right|} \\ &<\frac{B \frac{M^{2} \epsilon}{4 B}+B \frac{M^{2} \epsilon}{4 B}}{\frac{M^{2}}{2}} \\ &=\epsilon . \end{aligned}\]