\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\)
\(=2\times\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}\right)\)
\(=2\times\left(\dfrac{64+32+16+8+4+2+1}{192}\right)\)
\(=\dfrac{127}{96}\)
=2/3+1/3+1/6+1/12+1/24+1/48+1/96
=\(\dfrac{127}{96}\)