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Home » x^2 + y^2 = 5200 - Get link 4share

x^2 + y^2 = 5200 - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Solution:** To find the remainder when \( P(x) = x^4 - 5x^3 + 6x^2 + 4x - 8 \) is divided by \( x - 2 \), we use the Remainder Theorem, which states that the remainder of a polynomial \( P(x) \) divided by \( x - c \) is \( P(c) \).

📌 Here, \( c = 2 \). Calculate \( P(2) \):

📌 P(2) = (2)^4 - 5(2)^3 + 6(2)^2 + 4(2) - 8

📌 = 16 - 5 \times 8 + 6 \times 4 + 8 - 8

📌 = 16 - 40 + 24 + 8 - 8

📌 = 16 - 40 + 24

📌 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:

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