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what is the purpose of the preamble - ECD Germany

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 Therefore, the number is $oxed{14}$.

📌 Question: What is the remainder when the sum $1^3 + 2^3 + 3^3 + \dots + 10^3$ is divided by $9$?

📌 Solution: Use the formula for the sum of cubes:

📌 \left(\sum_{k=1}^{n} k^3

📌 ight) = \left(rac{n(n+1)}{2}

📌 For $n = 10$:

📌 \sum_{k=1}^{10} k^3 = \left(rac{10 \cdot 11}{2}

📌 ight)^2 = (55)^2 = 3025.

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