אתה תותח!! תודה על העזרה =) !
<math>\begin{align}
& \forall \varepsilon >0\to \varepsilon '=\frac{\varepsilon }{L+\varepsilon } \\
& \underset{n\to \infty }{\mathop{\lim }}\,b_{n}=0\wedge \underset{n\to \infty }{\mathop{\lim }}\,\frac{a_{n}}{b_{n}}=L \\
& \exists n_{1}\backepsilon N\to \forall i>n_{1}\to \varepsilon '<b_{i}<\varepsilon ' \\
& \exists n_{2}\backepsilon N\to \forall i>n_{2}\to -\varepsilon '<\frac{a_{i}}{b_{i}}-L<\varepsilon ' \\
& n_{0}=\max (n_{1},n_{2}) \\
& \forall i>n_{0}\to b_{i}<\varepsilon '\wedge -\varepsilon <\frac{a_{i}}{b_{i}}-L<\varepsilon \Rightarrow a_{i}-Lb_{i}<\varepsilon b_{i}\Rightarrow a_{i}<Lb_{i}+\varepsilon b_{i}\Rightarrow a_{i}<b_{i}(L+\varepsilon ) \\
& -\varepsilon <0<a_{i}<b_{i}(L+\varepsilon )<\varepsilon '(L+\varepsilon )=\frac{\varepsilon }{L+\varepsilon }(L+\varepsilon )=\varepsilon \\
& -\varepsilon <a_{i}<\varepsilon \Rightarrow \left| a_{i} \right|<\varepsilon \Rightarrow \underset{n\to \infty }{\mathop{\lim }}\,a_{n}=0 \\
\end{align}</math>
