What is the following value when expressed as a common fraction:
1/2 + 1/2^2 + 1/2^3 + ... + 1/2^8 + 1/2^9 + 1/2^10 + 1/2^11 + 1/2^12
Geometic sum
Common ratio = 1/2 = r
Sum
first term ( 1 - r^(n )) / (1 - r) =
(1/2 ( 1 - (1/2)^(12))/(1 -1/2) = 4095 / 4096
