How do you find the sum of the infinite geometric series 3 - 2 + 4/3 - 8/9 + ...? Precalculus Series Infinite Series 1 Answer Daniel L. Nov 10, 2015 The sum of this series is #1 4/5# Explanation: #a_1=3# #q=(a_2)/(a_1)=-2/3# Since #|q|<1#, the sequence is convergent, so we can calculate the sum using: #S=a_1/(1-q)=3/(1-(-2/3))=3/(1+2/3)=3/(5/3)=3*3/5=9/5=1 4/5# 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 6412 views around the world You can reuse this answer Creative Commons License