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Home » The solutions for \(\theta\) in the interval \([0^\circ, 360^\circ]\) are: - Abu Waleed Tea

The solutions for \(\theta\) in the interval \([0^\circ, 360^\circ]\) are: - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Set \(2a = 729\) → \(a = 364.5\)

📌 Then bottles: 364.5, 182.25, 91.125, 45.5625, 22.78125, 11.390625, 5.6953125, 2.84765625, 1.423828125, 0.7119140625, ...

📌 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 capacities* reaches 729? But total capacity is infinite.

📌 Given context, likely intended:

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