Summing 1 + 1/2 + 1/4 + 1/8 + ...

Algebra 2 · Axiom Academy

Evaluate a classic infinite geometric series using the sum formula . Find the sum of the infinite geometric series , where every term is half of the one before it. Nice work — you summed an infinite geometric series both numerically and algebraically. The pieces worth keeping: Geometric series test: consecutive terms share a constant ratio r — here . Convergence condition: an infinite geometric series has a finite sum only when . Zeno intuition: the partial sums close in on 2 — infinitely many terms, finite total. This same "sum of ever-shrinking pieces" idea reappears in repeating decimals, fractal geometry, and decay models.

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