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Home » You Won’t Believe How Logitech Keyboards Transform Your Typing Experience! - Dachbleche24

You Won’t Believe How Logitech Keyboards Transform Your Typing Experience! - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 The sum of the first \( n \) positive integers is given by the formula \( S = rac{n(n + 1)}{2} \). If the sum is 5050, find \( n \).

📌 Set up the equation: \( rac{n(n + 1)}{2} = 5050 \).

📌 Multiply both sides by 2: \( n(n + 1) = 10100 \).

📌 Solve the quadratic equation \( n^2 + n - 10100 = 0 \) using the quadratic formula \( n = rac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

📌 Here, \( a = 1, b = 1, c = -10100 \).

📌 Calculate the discriminant: \( 1^2 - 4 imes 1 imes (-10100) = 1 + 40400 = 40401 \).

📌 The square root of 40401 is 201.

📌 Calculate \( n \): \( n = rac{-1 \pm 201}{2} \).

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