Question

1/2+1/4+1/8+...+1/128

 

Answer 1

`1/2+1/4+1/8+...+1/128`

`=1/2x2+1/4x2+1/8x2+...+1/128x2`

`=1+1/2+1/4+1/8+...+1/64`

`=1+1/2+1/4+1/8+...+1/64-1/2-1/4-1/8-...-1/128`

`=1-1/128`

`=127/128`

Answer 2

\(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{128}\)

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

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

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