`P= 1/2^2 + 1/2^3 + 1/2^4 +....+1/2^99`
`1/2 P = 1/2( 1/2^2 + 1/2^3 + 1/2^4 +...+1/2^99)`
`1/2 P = 1/2^3 + 1/2^4 + 1/2^5+...+1/2^100)`
`P - 1/2P = 1/2^2 + 1/2^3 + 1/2^4+...+1/2^99 - 1/2^3 - 1/2^4 - 1/2^5 -...-1/2^100`
`1/2 P = 1/2^2 - 1/2^100`
`P= (1/2^2 - 1/2^100) : 1/2`
`P= (1/2^2 - 1/2^100) .2`
`P= 1/2 - 1/2^99`
Vậy `P= 1/2 - 1/2^99`