Take the positive root: \( n = \frac{30}{4} = 7.5 \). Since \( n \) must be an integer, the largest possible \( n \) is 7. Check \( S_7 \):

Sun, 03 May 2026 22:48:16 +0000

Title: Maximizing Integer Solutions: How to Take the Positive Root of \( n = \frac{30}{4} \) and Analyze \( S_7 \) In mathematical problem-solving, particularly when dealing with fractional results, choosing the correct root can significantly impact outcomes. A classic example is calculating \( n = \frac{30}{4} = 7.5 \). While this yields a decimal, real-world applications often require integer solutions—especially in discrete contexts like programming, resource allocation, or combinatorics. ### Why \( n = \frac{30}{4} = 7.5 \) Isn’t Kingdom-Ready Since \( n \) must be an integer, simply rounding or dropping the decimal has limitations. In many scenarios, the largest valid integer—representing the most viable solution—must be selected. For \( n = 7.5 \), this means the optimal integer value is 7. Choosing 7 ensures feasibility without violating constraints of whole numbers.