Question

Answer 1

\(E=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^8}\)

=> \(2E=1+\dfrac{1}{2}+...+\dfrac{1}{2^7}\)

=> \(2E-E=\left(1+\dfrac{1}{2}+...+\dfrac{1}{2^7}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^8}\right)\)

=>\(E=1-\dfrac{1}{2^8}=\dfrac{255}{256}\)