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benefits of ginger water with lemon - Imagemakers

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Therefore, the number of integers is $ \boxed{20} $.

📌 Question: What is the remainder when the sum $ 1^3 + 2^3 + 3^3 + \dots + 10^3 $ is divided by 7?

📌 Solution: We use the formula for the sum of cubes:

📌 \sum_{k=1}^{n} k^3 = \left( \frac{n(n+1)}{2} \right)^2

📌 For $ n = 10 $:

📌 \sum_{k=1}^{10} k^3 = \left( \frac{10 \cdot 11}{2} \right)^2 = (55)^2 = 3025

📌 Now compute $ 3025 \mod 7 $. First, reduce 55 modulo 7:

📌 \div 7 = 7 \text{ remainder } 6 \Rightarrow 55 \equiv 6 \pmod{7}

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