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Home » Michael Graves Misfits: The Revolutionary Designer No One Knew They Needed! - Upplift

Michael Graves Misfits: The Revolutionary Designer No One Knew They Needed! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 b_k = M\left( \frac{1}{k} \right) + M\left( \frac{2}{k} \right) + \cdots + M\left( \frac{k}{k} \right).

📌 Find $ b_k $ in simplest form.

📌 M(v) = v - \frac{v^4}{4},

📌 b_k = \sum_{j=1}^{k} M\left( \frac{j}{k} \right) = \sum_{j=1}^{k} \left( \frac{j}{k} - \frac{1}{4} \left( \frac{j}{k} \right)^4 \right).

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r = -rac{(5 - \sqrt{5})(\sqrt{5} + 1)}{(\sqrt{5} - 1)(\sqrt{5} + 1)}...
Thus, \( r = \sqrt{5} \) or \( r = -\sqrt{5} \). These correspond to p...
e 0\), and \(x
e y\) (to avoid division by zero in the original expression).
Check that \(x = \sqrt{5} y\):
Then \( rac{x+y}{x-y} = rac{\sqrt{5}+1}{\sqrt{5}-1} = rac{3+\sqrt{5...
Similarly for \(x = -\sqrt{5} y\):
\( rac{-\sqrt{5}+1}{-\sqrt{5}-1} = rac{\sqrt{5}-1}{\sqrt{5}+1} = ra...
Therefore, the solutions are all real pairs where \( x = \sqrt{5} y \)...
e 0 \). However, since the equation is symmetric in \((x,y)\) under th...

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