What is the geometric power series? Precalculus Series Convergence of Geometric Series 1 Answer Bill K. Dec 7, 2015 #a+ax+ax^{2}+ax^{3}+cdots#, which converges to #a/(1-x)# when #|x|<1#. More generally, you could also write #a+a(x-c)+a(x-c)^{2}+a(x-c)^{3}+cdots#, which converges to #a/(1-(x-c))=a/((1+c)-x)# when #|x-c| < 1#. Answer link Related questions What are some examples of infinite geometric series? How can I tell whether a geometric series converges? How do I write a repeating decimal as an infinite geometric series? Can a repeating decimal be equal to an integer? How do I find the sum of the infinite geometric series #2/3#, #- 4/9#, ...? How do I find the sum of the infinite geometric series such that #a_1=-5# and #r=1/6#? What is the sum of the infinite geometric series with #a_1=42# and #r=6/5#? What is the sum of the infinite geometric series 8 + 4 + 2 + 1 +... ? What is the sum of the infinite geometric series 1 + #1/5# + #1/25# +... ? How do I find the sum of the infinite geometric series #1/2# + 1 + 2 + 4 +... ? See all questions in Convergence of Geometric Series Impact of this question 2211 views around the world You can reuse this answer Creative Commons License