Finite geometric series: Hi, I want to ask a question, is about... for example, take the sequence 1,2,4,8,... Notice that each number is twice the value of the previous number. So, a number in the sequence can be represented by the function f(n) = 2^n-1. One way to write the sum of the sequence through the 5th number in the sequence is E^5 n-1^2n-1. This equation can also be written as S5 = 2^0 + 2^1+2^2+2^3+2^4. If we multiply this equation by 2, the equation becomes 2(S5) = 2^1+2^2+2^3+2^4+2^5.
What happens if I subtract the two equations and solve for S5? Can I use this information to come up with a way to find any geometric series Sn in the form E^a n-1^bn-1?