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Home » Pokémon Z Reviews That Are Getting Millions of Views — Are You Missing Out? - Midis

Pokémon Z Reviews That Are Getting Millions of Views — Are You Missing Out? - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Question:** A mathematician is analyzing a topological space and needs to compute the sum of the series \( \sum_{k=1}^{50} \frac{1}{k(k+1)} \) as part of a homology calculation. Calculate this sum.

📌 Solution:** The given series is \( \sum_{k=1}^{50} \frac{1}{k(k+1)} \). We can simplify the terms using partial fraction decomposition:

📌 \frac{1}{k(k+1)} = \frac{A}{k} + \frac{B}{k+1}

📌 Solving \( 1 = A(k+1) + Bk \), we equate coefficients:

📌 \( A + B = 0 \)

📌 \( A = 1 \)

📌 Thus, \( B = -1 \). So,

📌 The series becomes telescoping:

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\[ \ln(4) = 200r \]
Calculate \( \ln(4) \):
\[ \ln(4) \approx 1.3863 \]
\[ r = \frac{1.3863}{200} \approx 0.0069315 \]
\[ r \approx 0.69315\% \]
#### 0.0069315
A science journalist is analyzing the impact of solar panel installati...
Initial efficiency, \( E_0 = 18\% \)
Annual growth rate, \( r = 2\% = 0.02 \)
Time, \( t = 15 \) years

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