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Home » You Wont Believe What Fantasylabs Does—Unlock Magic You Never Knew Existed! - Coaching Toolbox

You Wont Believe What Fantasylabs Does—Unlock Magic You Never Knew Existed! - Coaching Toolbox

📅 May 6, 2026 👤 scraface

May 06, 2026

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Now substitute $ u = x^2 - 2 $ into $ f $:
f(x^2 - 2) = (x^2 - 2)^2 - 1 = x^4 - 4x^2 + 4 - 1 = x^4 - 4x^2 + 3.
\boxed{x^4 - 4x^2 + 3}
Question: Compute $ \sum_{n=1}^{50} \frac{1}{n(n+2)} $.
Solution: We begin by simplifying the general term using partial fract...
\frac{1}{n(n+2)} = \frac{A}{n} + \frac{B}{n+2}.
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{...

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