we are given
[tex] \sum _{i=1}^8\:2^{i-1} [/tex]
we can expand it
[tex] \sum _{i=1}^8\:2^{i-1}=2^{1-1}+2^{2-1}+2^{3-1}+2^{4-1}+2^{5-1}+2^{6-1}+2^{7-1}+2^{8-1} [/tex]
[tex] \sum _{i=1}^8\:2^{i-1}=2^{0}+2^{1}+2^{2}+2^{3}+2^{4}+2^{5}+2^{6}+2^{7} [/tex]
we can simplify it
and we get
[tex] \sum _{i=1}^8\:2^{i-1}=255 [/tex]............Answer
