Repeated halving from $1/2$ onward sums exactly to $1$.Suggest a slogan
\[ \sum_{k=1}^\infty \frac{1}{2^k} = 1. \]
The partial sums are \(\sum_{k=1}^N 2^{-k} = 1-2^{-N}\), which converge to \(1\) as \(N\to\infty\).
The geometric series $\sum_{k=1}^\infty 2^{-k}$ sums to one
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