Suppose $\{Z_{i}\}_{i=1,2,\ldots}$ are normally distributed (identically and independent) random variables with mean $\mu>0$ and positive variance $\sigma^{2}$. Suppose we want to calculate the probability, that $$U(n)=u+\sum_1^nZ_i\le0 \text{ for some }n\in\mathbb{N}\text{, where }u>0\text{.}$$

According to risk of ruin wikipedia page, the probability for such setting can be approximated by

$$\left( \frac{2}{1+\frac{\mu}{r}}-1 \right)^{u/r}$$ where $$r=\sqrt{\mu^2+\sigma^2}\text{.}$$ However, I cannot find any proof/derivation for this result. I am grateful for any advice on how to approach this problem!