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Home » Better: adjust to make whole numbers. New version: - Tacotoon

Better: adjust to make whole numbers. New version: - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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w = 50 - 25 = 25
The maximum area is:
A = 25 \times 25 = 625
Thus, the maximum possible area is:
\boxed{625}
Compute \(\sum_{k=1}^{50} \frac{1}{k(k+1)}\).
The given sum can be simplified using partial fraction decomposition:
\frac{1}{k(k+1)} = \frac{1}{k} - \frac{1}{k+1}
Thus, the sum becomes a telescoping series:
\sum_{k=1}^{50} \left( \frac{1}{k} - \frac{1}{k+1} \right)

📝 Recent Posts

Increase = 40% of 5,000 = 0.4 × 5,000 = 2,000
Total infected after one week = 5,000 + 2,000 = 7,000
A palynologist finds that in a 10,000-year-old sediment core, 12% of p...
Pine pollen grains = 12% of 25,000 = 0.12 × 25,000 = 3,000
A linguist analyzing historical texts observes that a grammatical cons...
Historical rate = 1 per 2,500 words → 150,000 / 2,500 = 60 expected
Actual = 90
Frequency multiplier = 90 / 60 = 1.5
An epidemiologist models a disease with a basic reproduction number R₀...
Generation 1: 1 person → infects 2.5

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