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why is the flag at half staff today in utah - ClickBalance

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 We require $n_k \leq 100$:

📌 7k - 4 \leq 100 \Rightarrow 7k \leq 104 \Rightarrow k \leq rac{104}{7} pprox 14.857.

📌 So the largest integer $k$ is $14$.

📌 Thus, there are $14$ such numbers.

📌 Check: $n_{14} = 7(14) - 4 = 98 - 4 = 94 \leq 100$, and $n_{15} = 7(15) - 4 = 105 - 4 = 101 > 100$.

📌 So only $14$ terms.

📌 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 $9$?

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