Each rings gives you a raw +15% chance, so the value is 0.15
If you feed that into the evasion formula you get
$$evadeChance(n)=0.999\cdot\frac{0.15n}{0.15n + 1}$$
A few example points
With 1 ring:
raw value = 0.15
$$
\text{evadeChance} \approx 0.999 \cdot \frac{0.15}{1.15} \approx 0.13%
$$
10 rings:
raw value = 1.5
$$
\text{evadeChance} \approx 0.999 \cdot \frac{1.5}{1.5 + 1} \approx 0.60%
$$