1994•Unpublished venueRequires access
Summation of Series, Taylor Series
Peter Turner
Open publisher page 1 citations
Abstract
A geometric series 1+x+ x 2 +...= ∑ i=0 ∞ x i ]] <![CDATA[$$1 + x + {x^2} + ... = \sum\nolimits_{i = 0}^\infty {{x^i}} \]$$ is convergent if its common ratio x satisfies |x| < 1. It is divergent if |x| ≥ 1. For a convergent geometric series, its sum is known in closed form: 3.1.1 1+x+ x 2 +...= ∑ i=0 ∞ x i = 1 1−x (|x|≺1) ]] <![CDATA[$$1 + x + {x^2} + ... = \sum\limits_{i = 0}^\infty {{x^i}} = \frac{1}{{1 - x}}(|x| \prec 1)$$