Half of a Series

Algebra Level 1

It is well known that
\[ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots = 1. \] Now, the figure on the right shows a square successively divided into half.

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If we color the successively smaller squares blue, as shown on the left, what fraction of the largest square is shaded blue?

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