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Home » What Makes This Sonic Character a Legend? The Ultimate Breakdown! - Upplift

What Makes This Sonic Character a Legend? The Ultimate Breakdown! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 If the sum of the first \(n\) natural numbers is given by \(\frac{n(n+1)}{2}\), find \(n\) when the sum is 210.

📌 Set up the equation: \(\frac{n(n+1)}{2} = 210\).

📌 Multiply by 2: \(n(n+1) = 420\).

📌 Solve \(n^2 + n - 420 = 0\) using the quadratic formula:

📌 \(n = \frac{-1 \pm \sqrt{1 + 1680}}{2} = \frac{-1 \pm 41}{2}\).

📌 The positive solution is \(n = 20\).

📌 A triangle has sides of lengths 7, 24, and 25. Verify if it is a right triangle using the Pythagorean theorem.

📌 Check \(7^2 + 24^2 = 25^2\).

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