The sum of the first \(n\) terms in the infinite geometric sequence \(\left\{\frac{1}{4},\frac{1}{8},\frac{1}{16},\dots \right\}\) is \(\frac{255}{512}\) . Find \(n\).
We have that
255/512 = (1/4) [ 1 - (1/2)^n ] / [ 1 - 1/2] simplify
255/512 = (1/2) [ 1 - (1/2)^n ]
255 / 256 = 1 - (1/2)^n
(1/2)^n = 1 - 255/256
(1/2)^n = 1/256
(1/2)^n = (1/2)^8
So....n = 8
+885 
