We can determine this to be a Geometric Sequence with:
a = 2
r = 1/2
an = ?
We must first find an. We know that an = 1/256, therefore we can use this formula to discover an:
an = a r^n-1
1/256 = 2 1/2^n-1
1/256 / 2 = 1/2^n-1
1/512 = 1/2^n-1
log(1/512) = log(1/2^n-1)
9 = n - 1
10 = n
Therefore, we know an = 10
Now we input it into this equation and solve:
Sn = a(1-r^n/1-r)
Sn = 2(1-1/2^10/1-1/2)
Sn = 2(1023/1024 / 1 / 2)
Sn = 2(1023/1024 * 2 / 1)
Sn = 2(2046/1024)
Sn = 2(1023/512)
Sn = 1023/256
Sn = 3.992
Geez, that took awhile... xD
