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Home » This Simple Math Hack Will Save You Time in the Kitchen—Here’s Half of 3/4 Cup! - AMAZONAWS

This Simple Math Hack Will Save You Time in the Kitchen—Here’s Half of 3/4 Cup! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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Question: Compute $ \sum_{n=1}^{50} \frac{1}{n(n+2)} $.
Solution: We begin by simplifying the general term using partial fract...
\frac{1}{n(n+2)} = \frac{A}{n} + \frac{B}{n+2}.
Multiplying both sides by $ n(n+2) $:
= A(n+2) + Bn.
= An + 2A + Bn = (A + B)n + 2A.
A + B = 0, \quad 2A = 1 \Rightarrow A = \frac{1}{2}, \quad B = -\frac{...
\frac{1}{n(n+2)} = \frac{1}{2} \left( \frac{1}{n} - \frac{1}{n+2} \rig...
\sum_{n=1}^{50} \frac{1}{n(n+2)} = \frac{1}{2} \sum_{n=1}^{50} \left(...
This is a telescoping sum. Write out the first few terms:

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