2+2²+2³+....+$2^{2010}$
=( 2+2²)+( 2³+$2^{4}$)+....+( $2^{2009}$+$2^{2010}$)
=2.(1+2)+2³.(1+2)+...+$2^{2009}$.(1+2)
=2.3+2³+3+...+$2^{2009}$.3
=3.(2+2³+...+$2^{2009}$)⋮ 3 (đpcm)
2+2²+2³+....+$2^{2010}$
=( 2+2²+ 2³)+....+($2^{2008}$+$2^{2009}$+$2^{2010}$)
=2.(1+2+2²)+...+$2^{2008}$.(1+2+2²)
=2.7+...+$2^{2008}$.7
=7.(2+...+$2^{2008}$)⋮ 7 (đpcm)