A=\(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}\)

128A=64+32+16+8+4+2+1

128A=127

A=\(\dfrac{127}{128}\)

For : \(A=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}\)

\(\Rightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{4}+.....+\dfrac{1}{128}\)

\(\Rightarrow2A-A=1-\dfrac{1}{128}\)

\(\Rightarrow A=\dfrac{127}{128}\)

For : A=12+14+18+132+164+1128

⇒2A=1+12+14+.....+1128

⇒2A−A=1−1128

⇒A=127128