`A = 2^100 - 2^99 + 2^98 - 2^97 + .... + 2^2 - 2`
`2A = 2^101 - 2^100 + 2^99 - 2^98 + .... + 2^3 - 2^2`
`2A + A = ( 2^101 - 2^100 + 2^99 - 2^98 + .... + 2^3 - 2^2 ) + ( 2^100 - 2^99 + 2^98 - 2^97 + .... + 2^2 - 2 )`
`3A = 2^101 - 2`
`A = ( 2^101 - 2 ) : 3`
`A = ( 2^101 - 2 )/3`