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Home » \sum_k=1^50 \frac1k(k+2) - Parker Core Knowledge

\sum_k=1^50 \frac1k(k+2) - Parker Core Knowledge

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 The sum of all real solutions to the equation \( |2x - 5| = |x + 3| \) is?

📌 Use the property \( |A| = |B| \Rightarrow A = B \) or \( A = -B \).

📌 Case 1: \( 2x - 5 = x + 3 \Rightarrow x = 8 \)

📌 Check: LHS = |16 - 5| = 11, RHS = |8 + 3| = 11 → valid.

📌 Case 2: \( 2x - 5 = -(x + 3) \Rightarrow 2x - 5 = -x - 3 \Rightarrow 3x = 2 \Rightarrow x = \frac{2}{3} \)

📌 Check: LHS = |4/3 - 5| = |-11/3| = 11/3, RHS = |2/3 + 3| = |11/3| = 11/3 → valid.

📌 Sum = \( 8 + \frac{2}{3} = \frac{24}{3} + \frac{2}{3} = \frac{26}{3} \)

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