What is the sum of the first six terms of the series?
32−8+2−0.5+...
Enter your answer as a simplified fraction in the box.
Every successive term is -(1/4) * previous term = r
The sum is
first term ( 1 - r^6) /( 1 - r) =
32 ( 1 - (-1/4)^6) / (1 - - 1/4) =
32 ( 1 - (-1/4)^6) / ( 5/4) =
32 ( 4/5) ( 1 - (-1/4)^6) =
128 /5 * ( 1 - (-1/4)^6 ) =
819 / 32
