# 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