Let's play everyone's favourite Thanksgiving game, "spot the pattern" (boo.. no turkey emoticon)!austin wrote:1/2+1/4+1/8+...+1/512=?
A.0<S<1/2
B.1/2<S<1
C.1<S<3/2
D. 3/2<S<2
E. 2<S<5/2
1/2 + 1/4 = 3/4
3/4 + 1/8 = 7/8
7/8 + 1/16 = 15/16
As we progress, we're getting closer and closer to 1, but we're never actually going to get there. So, the sum of the sequence will be less than 1, but more than the 1/2 we start with: choose (B).
If anyone actually cares about the math, the generic formula for this particular sequence is:
Sum(first n terms) = (2^n - 1)/2^n
So, if we have 9 terms (512 = 2^9), the sum is:
(2^9 - 1)/2^9 = 511/512
