\(E= (\dfrac{2}{2}-\dfrac{1}{2})+(\dfrac{1}{2}-\dfrac{1}{4})+(\dfrac{1}{4}-\dfrac{1}{8})+(\dfrac{1}{8}-\dfrac{1}{16})+(\dfrac{1}{16}-\dfrac{1}{32})+(\dfrac{1}{32}-\dfrac{1}{64})+(\dfrac{1}{64}-\dfrac{1}{128})+(\dfrac{1}{128}-\dfrac{1}{256})+(\dfrac{1}{256}-\dfrac{1}{512})\)
\(E=\dfrac{2}{2}-\dfrac{1}{512}\)
\(E=\dfrac{511}{512}\)