The pillar of Infinity

Algebra Level 3

The fraction \(\frac{1}{2}\) grows every second in the following manner:

\[\large \frac{1}{2} \to \large{ \frac{\frac{1}{4}}{\frac{2}{8}}} \to \huge{\frac{\frac{\frac{1}{4}}{\frac{4}{16}}}{\frac{\frac{2}{8}}{\frac{8}{32}}}}\]

Given that the expression at time \(t=0\) is \(\frac12\) and grows every second to the next expression in the same pattern as above. Find the sum of all the expressions formed till \(3600\) seconds. ​


This question is part of the set All-Zebra

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