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Home » The sum of the first \(n\) positive integers is 5050. Find \(n\). - 500apps

The sum of the first \(n\) positive integers is 5050. Find \(n\). - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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f(3) = 2(3)^2 - 12(3) + 18 = 2(9) - 36 + 18 = 18 - 36 + 18 = 0
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We are to compute:
\sum_{k=1}^{50} \frac{1}{k(k+2)}
We use partial fraction decomposition:
\frac{1}{k(k+2)} = \frac{A}{k} + \frac{B}{k+2}
Multiplying both sides by \(k(k+2)\):
Set \(k = 0\): \(1 = A(2) \Rightarrow A = \frac{1}{2}\)

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