Home/Calculus II/Sequences and series/Geometric seriesSection 14.3Geometric seriesFormulaCopy LaTeX∑n=0∞arn\sum_{n=0}^{\infty}ar^nn=0∑∞arnView detail →converges if ∣r∣<1|r|<1∣r∣<1, andFormulaCopy LaTeX∑n=0∞arn=a1−r.\sum_{n=0}^{\infty}ar^n=\frac{a}{1-r}.n=0∑∞arn=1−ra.View detail →If ∣r∣≥1|r|\ge1∣r∣≥1, it diverges.