Chứng minh 2 mũ 1+2 mũ 2+2 mũ 3+…..+2 mũ 2010 chia hết cho 3 và 7 Giúp em vs 16/08/2021 Bởi Lydia Chứng minh 2 mũ 1+2 mũ 2+2 mũ 3+…..+2 mũ 2010 chia hết cho 3 và 7 Giúp em vs
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) Bình luận
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)