What is a convergent infinite series? Calculus Tests of Convergence / Divergence Infinite Series 1 Answer Wataru Oct 29, 2014 An infinite series #sum_{i=1}^infty a_i# is said to be convergent if #lim_{n to infty}S_n# exists, where #S_n=a_1+a_2+a_3+cdots+a_n#. I hope that this was helpful. Answer link Related questions How can an infinite series have a finite sum? How do you evaluate an infinite series? How do you find the sum of an infinite series? How does an infinite geometric series apply to being pushed on a swing? What are infinite series used for? What is a divergent infinite series? What is a partial sum of an infinite series? What is an oscillating infinite series? What is a telescoping infinite series? What is a collapsing infinite series? See all questions in Infinite Series Impact of this question 2351 views around the world You can reuse this answer Creative Commons License