How do you know when a geometric series converges? Calculus Tests of Convergence / Divergence Geometric Series 1 Answer Wataru Sep 22, 2014 A geometric series #sum_{n=0}^inftyar^n# converges to #a/{1-r}# if #|r|<1#. Answer link Related questions What is a Geometric Series? How do you find #a_1# for the geometric series with #r=3# and #s_6=364#? How do you find the sum of finite geometric series? How do you find the sum of the geometric series #8+4+2+1+…#? How do you use a geometric series to prove that #0.999…=1#? What is #s_n# of the geometric series with #a_1=4#, #a_n=256#, and #n=4#? What is the formula for the sum of an infinite geometric series? How do you know when to use the geometric series test for an infinite series? How do you find the sum of the infinite geometric series with #a_1=-5# and #r=1/6#? How do you find the common ratio of an infinite geometric series? See all questions in Geometric Series Impact of this question 6267 views around the world You can reuse this answer Creative Commons License