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Subtrahiere 7 von beiden Seiten: - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Given that $ a + b + c = 0 $, substitute into the identity:
a^3 + b^3 + c^3 - 3abc = 0 \cdot (a^2 + b^2 + c^2 - ab - bc - ca) = 0.
a^3 + b^3 + c^3 = 3abc.
This completes the proof.
oxed{a^3 + b^3 + c^3 = 3abc}
Question: Compute $ \sum_{k=1}^{50} rac{1}{k(k+2)} $.
Solution: We evaluate the sum:
\sum_{k=1}^{50} rac{1}{k(k+2)}.
We use partial fractions:
rac{1}{k(k+2)} = rac{A}{k} + rac{B}{k+2}.

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