+865 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.
+23246 The formula for the sum of the first n terms of a geometric series is: Sum = a(1 - rn) / (1 - r)
where a = first term = ¼ r = common ratio = ½ n = number of terms
---> 255/512 = (¼)·( 1 - (½)n ) / ( 1 - ½ )
---> 255/512 = (¼)·( 1 - (½)n ) / ( ½ )
---> 255/512 = (½)·( 1 - (½)n )
---> 255/256 = 1 - (½)n
---> (½)n = 1 - 255/256
---> (½)n = 1/256
---> (½)n = (1/2)8
---> n = 8
