Answer:
255
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
1[tex](2)^{n-1}[/tex] ← is the n th term
with a = 1 and r = 2
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex], thus
[tex]S_{8}[/tex] = [tex]\frac{1(2^8-1)}{2-1}[/tex]
= [tex]2^{8}[/tex] - 1 = 256 - 1 = 255
