In the RMSProp optimization algorithm, the effective observation window for the exponentially weighted average of squared gradients is defined by the quantity $\frac{1}{1 - \gamma}$, where $\gamma$ is the weighting term (or decay factor). This means the state variable aggregates information over approximately the past $\frac{1}{1 - \gamma}$ observations. A larger $\gamma$ produces a longer memory and a smoother average, while a smaller $\gamma$ makes the algorithm more responsive to recent gradients. For example, setting $\gamma = 0.9$ yields an effective window of $\frac{1}{1 - 0.9} = 10$ observations.