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Geometric Series — Sum and Convergence

Σ ar^n = a/(1−r) for |r|<1 (converges). Diverges if |r|≥1. Partial sum: S_n = a(1−r^n)/(1−r).

CalculusCommon Core LIM-7.ASERVerified correct ✓

Worked examples

Find the sum of the infinite geometric series with first term a = 1 and common ratio r = -1/2. (Assume the series converges; use S = a / (1 − r).)
Answer: 0.6667
Find the sum of the infinite geometric series with first term a = 2 and common ratio r = 1/2. (Assume the series converges; use S = a / (1 − r).)
Answer: 4

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