$$S(n)=1+\frac{1}{2}+\frac{1}{3}+\dots+\frac{1}{n}$$

$$\dot{x}=\frac{v_1 x}{l+v_1 t}+v_0$$

$$\frac{dy}{d\tau}=\frac{y}{\tau}+v_0$$

$$\frac{du}{dv}=v_0$$

$$u=v_0 v-v_0 \ln l;\frac{y}{\tau}=v_0 \ln \tau-v_0 \ln l$$

$$\ln\left(1+\frac{v_1 t}{l}\right)=\frac{v_1 x}{v_0 (l+v_1 t)}$$

$$\ln\left(1+\frac{v_1 t}{l}\right)=\frac{v_1}{v_0}$$

$$\ln\left(1+t\right)=10000$$
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