\(\frac{1+2+2^2+...+2^{2008}}{1-2^{2008}}\)
Ta có: Đặt A = 1 + 2 + 22 + ... + 22008
2A = 2 + 22 + 23 + ... + 22009
2A - A = (2 + 22 + 23 + ... + 22009) - (1 + 2 + 22 + ... + 22008)
A = 22009 - 1
=> \(\frac{1+2+2^2+...+2^{2008}}{1-2^{2008}}=\frac{2^{2009}-1}{1-2^{2008}}\)