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📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Substituting into the expression:
x^4 + 4x^2 + 3 = (u^2 - 4u + 4) + 4(u - 2) + 3 = u^2 - 4u + 4 + 4u - 8...
f(u) = u^2 - 1.
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) $:

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