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Home » Thus, the ratio is \(\boxed\frac\pi \sqrt372\). - Dachbleche24

Thus, the ratio is \(\boxed\frac\pi \sqrt372\). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 = \frac{1}{n} \sum_{k=1}^{n} k - \frac{1}{3n^3} \sum_{k=1}^{n} k^3

📌 Use formulas:

📌 $ \sum_{k=1}^{n} k = \frac{n(n+1)}{2} $

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

📌 a_n = \frac{1}{n} \cdot \frac{n(n+1)}{2} - \frac{1}{3n^3} \cdot \left( \frac{n(n+1)}{2} \right)^2

📌 = \frac{n+1}{2} - \frac{1}{3n^3} \cdot \frac{n^2(n+1)^2}{4}

📌 Simplify the second term:

📌 \frac{1}{3n^3} \cdot \frac{n^2(n+1)^2}{4} = \frac{(n+1)^Question: A historian studying ancient navigation techniques discovers a triangular chart used by early mariners, with side lengths of $13$, $14$, and $15$ units. What is the length of the shortest altitude in this triangle?

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\(25 + 49 = 100\)
\(74
eq 100\)
Since the equation does not hold, it is not a right triangle.
#### Not a right triangle
Question:** A company offers a 15% discount on a product that original...
\(250 - (15\% imes 250) = 250 - 37.5 = 212.5\)
Price after tax:
\(212.5 + (8\% imes 212.5) = 212.5 + 17 = 229.5\)
#### 229.5

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