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Home » Do Eagles Fans Know This Game-Changing Strategy Is Changing the Fan Game? - Leaselab

Do Eagles Fans Know This Game-Changing Strategy Is Changing the Fan Game? - Leaselab

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 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 fractions:

📌 \frac{1}{n(n+2)} = \frac{A}{n} + \frac{B}{n+2}.

📌 Multiplying both sides by $ n(n+2) $:

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b_4 = F\left(rac{3}{8}
ight) = rac{3}{8} - rac{1}{2} \left(rac{3}{8}
ight)^2 = rac{3}{8} - rac{1}{2} \cdot rac{9}{64} = rac{3}{8} - ra...
b_5 = F\left(rac{39}{128}
ight) = rac{39}{128} - rac{1}{2} \left(rac{39}{128}
ight)^2 = rac{39}{128} - rac{1}{2} \cdot rac{1521}{16384} = rac{39...
Convert $ rac{39}{128} $ to denominator 32768:
rac{39}{128} = rac{39 \cdot 256}{128 \cdot 256} = rac{9984}{32768}
Now subtract:
b_5 = rac{9984 - 1521}{32768} = rac{8463}{32768}

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