`A = 1 + 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^2012`
`2A = 2 + 1 + 1/2 + 1/2^2 + ... + 1/2^2011`
`2A - A = ( 2 + 1 + 1/2 + 1/2^2 + ... + 1/2^2011 ) - ( 1 + 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^2012 )`
`A = 2 - 1/2^2012`
`A = 2^2013/2^2012 - 1/2^2012`
`A = ( 2^2013 - 1 )/2^2012`