Question 241243
S= a + ar + ar^2 + ar^3 + ... + ar^(n-1)(The series stops at n-1 power because there are n terms, but the first one is not multiplied by r) 
rS=ar +ar^2 + ar^3 + . . . + ar^n


Subtract the above equations.  All the middle terms subtract out!

S-rS = a - ar^n   


Factor out the S on the left and the a on the right side of the equation:

S(1-r) = a(1-r^n)


Divide both sides by (1-r):

{{{S=(a(1-r^n))/(1-r)}}}


This does not agree exactly with your final answer, so multiply both numerator and denominator by -1, and it will give you the final result you are looking for!


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus