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📅 May 6, 2026 👤 scraface

May 06, 2026

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📝 Recent Posts

Set \(2a = 729\) → \(a = 364.5\)
Then bottles: 364.5, 182.25, 91.125, 45.5625, 22.78125, 11.390625, 5.6...
Sum after n terms: \(S_n = a(1 - (1/2)^n)/(1 - 1/2) = 2a(1 - 2^{-n})\)
Set \(2a = 729\), so \(S_n = 729(1 - 2^{-n})\)
We want to fill 729 ml, so \(729(1 - 2^{-n}) \geq 729\) → only when n→...
Not helpful.
Instead, question is: How many bottles are needed until the *sum of ca...
Given context, likely intended:
A sequence where each bottle holds half the previous, starting with 72...
This is not working.

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