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Home » 🔥 Discover the HIDDEN Bonus Questions That Boost Your Test Scores! - Midis

🔥 Discover the HIDDEN Bonus Questions That Boost Your Test Scores! - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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Solution: We are looking for integers $ n $ such that $ n \equiv 2 \pm...
The sequence of such numbers is $ 2, 7, 12, \dots, $ forming an arithm...
Let the general term be $ a_k = 2 + (k - 1) \cdot 5 = 5k - 3 $.
We want $ a_k \leq 100 $, so:
5k - 3 \leq 100 \Rightarrow 5k \leq 103 \Rightarrow k \leq \frac{103}{...
Thus, $ k = 1, 2, \dots, 20 $, so there are 20 such numbers.
Therefore, the number of integers is $ \boxed{20} $.
Question: What is the remainder when the sum $ 1^3 + 2^3 + 3^3 + \dots...
Solution: We use the formula for the sum of cubes:
\sum_{k=1}^{n} k^3 = \left( \frac{n(n+1)}{2} \right)^2

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