`S=1/4+1/4^2+1/4^3+...+1/4^50`
`=> 1/4 S = 1/4(1/4+1/4^2+1/4^3+...+1/4^50)`
`⇒ 1/4 S = 1/4^2 + 1/4^3 + 1/4^4 +...+ 1/4^51`
`⇒ S - 1/4 S = (1/4+1/4^2+1/4^3+...+1/4^50)-(1/4^2 + 1/4^3 + 1/4^4 +...+ 1/4^51)`
`⇒ 3/4 S = 1/4 - 1/4^51`
`⇒ S = (1/4 - 1/4^51) : 3/4`
`⇒ S = (1/4 - 1/4^51) . 4/3`
`⇒ S = 1/3 - 1/(4^50 . 3)`