Geometric sequences and series
Set the first term, common ratio and number of terms to see each term, the sum and whether it converges.
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Questions students ask
When does a geometric series have a sum to infinity?
Only when the common ratio is between −1 and 1, so the terms shrink towards zero.
What formula does it use?
uₙ = arⁿ⁻¹; Sₙ = a(1 − rⁿ)/(1 − r); S∞ = a/(1 − r) for |r| < 1.
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