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Home » What Lurks in the Hole of Fear? Scientists Uncover Terrifying Secrets You Need to Know! - jntua results

What Lurks in the Hole of Fear? Scientists Uncover Terrifying Secrets You Need to Know! - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \boxed{(2x - 3)^2}

📌 Two proposed transit routes are modeled by the lines \( 3x - 4y = 12 \) and \( 2x + 5y = 10 \). Find their intersection point.

📌 3x - 4y = 12 \quad \text{(1)}\\

📌 2x + 5y = 10 \quad \text{(2)}

📌 Use elimination. Multiply equation (1) by 5 and equation (2) by 4:

📌 15x - 20y &= 60 \quad \text{(from (1))\times 5} \\

📌 8x + 20y &= 40 \quad \text{(from (2))\times 4}

📌 \end{aligned}

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Multiplying both sides by $ n(n+2) $:
= A(n+2) + Bn.
= An + 2A + Bn = (A + B)n + 2A.
A + B = 0, \quad 2A = 1 \Rightarrow A = \frac{1}{2}, \quad B = -\frac{...
\frac{1}{n(n+2)} = \frac{1}{2} \left( \frac{1}{n} - \frac{1}{n+2} \rig...
\sum_{n=1}^{50} \frac{1}{n(n+2)} = \frac{1}{2} \sum_{n=1}^{50} \left(...
This is a telescoping sum. Write out the first few terms:
\left( \frac{1}{1} - \frac{1}{3} \right) + \left( \frac{1}{2} - \frac{...
\frac{1}{2} \left( 1 + \frac{1}{2} - \frac{1}{51} - \frac{1}{52} \righ...
Compute the sum:

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