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Home » Can we have a non-path configuration with exactly 2 close pairs? - Carbonext

Can we have a non-path configuration with exactly 2 close pairs? - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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The sum of the first \( n \) positive integers is 210. What is \( n \)...
Use the formula \( \frac{n(n+1)}{2} = 210 \).
Multiply both sides by 2: \( n(n+1) = 420 \).
Solve the quadratic: \( n^2 + n - 420 = 0 \).
Factor: \( (n - 20)(n + 21) = 0 \).
Positive solution: \( n = 20 \).
A car depreciates in value by 15% per year. If it is worth $20,000 now...
Use exponential decay: \( V = 20000 \times (1 - 0.15)^3 \).
Compute \( 0.85^3 = 0.614125 \).
Then, \( V = 20000 \times 0.614125 \approx 12282.50 \).

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