How do you find the sum of the infinite geometric series 2+2/3+2/9+2/27+...? Precalculus Series Infinite Series 1 Answer Ratnaker Mehta Jul 10, 2016 3. Explanation: Let s denote the reqd. sum. Then, we know that, s=a/(1-r), where, a= the first term of the series, and, r,common ratio, with |r|<1. Here, a=2, and r=second term/first term=(2/3)/2=1/3, hence |r|<1. Therefore, s=2/(1-1/3)=2/(2/3)=3 Answer link Related questions What are some examples of infinite series? Can an infinite series have a sum? What are some examples of convergent series? What are common mistakes students make with infinite series? How do I use an infinite series to find an approximation for pi? How do I find the sum of the infinite series 1 + 1/5 + 1/25 +... ? How do I find the sum of the infinite series 1/2 + 1 + 2 + 4 +... ? What are some examples of divergent series? How do you find the sum of the infinite geometric series 1/2+1/4+1/8+1/16..? How do you find the sum of the infinite geometric series 3-1+1/3...? See all questions in Infinite Series Impact of this question 5269 views around the world You can reuse this answer Creative Commons License