1. The problem is to understand and interpret the given formula: $$\zeta(s) \approx \sum_{n=1}^{V} \frac{1}{n^s} + \beta(V,s) \cdot V^{1-s}$$ 2. The formula represents an approximation of the Riemann zeta function $\zeta(s)$, which is a key function in number theory and complex analysis. 3. The first term, $\sum_{n=1}^{V} \frac{1}{n^s}$, is a finite sum of powers, summing from $n=1$ to $V$, a positive integer cutoff. 4. The second term, $\beta(V,s) \cdot V^{1-s}$, acts as a correction or remainder term that adjusts the finite sum to better approximate the infinite series definition of $\zeta(s)$. 5. This expression is a known approximation used to truncate the infinite series while controlling the error by the term involving $\beta(V,s)$. Final answer: The formula approximates $\zeta(s)$ by using a finite partial sum plus a correction term depending on $V$ and $s$.