Toán Lớp 6: cho a = 1 + 2 mũ 1 + 2 mũ 2 + 2 mũ 3 + vân vân + 2 mũ 98 Chứng minh a chia hết cho 7

Question

Toán Lớp 6:  cho a = 1 + 2 mũ 1 + 2 mũ 2 + 2 mũ 3 + vân vân + 2 mũ 98 Chứng minh a chia hết cho 7

thienthanh · Answer

A = 1 + 2^1 + 2^2 + 2^3 + ... + 2^98   => A = ( 1 + 2^1 + 2^2 ) + ( 2^3 + 2^4 + 2^5 ) + ... + ( 2^96 + 2^97 + 2^98 )   => A = 1 . ( 1 + 2^1 + 2^2 ) + 2^3 . ( 1 + 2^1 + 2^2 ) + ... + 2^96 . ( 1 + 2^1 + 2^2 )   => A = 1 . 7 + 2^3 . 7 + ... + 2^96 . 7   => A = 7 . ( 1 + 2^3 + ... + 2^96 )  vdots 7   Vậy A  vdots 7    #dtkc

trucoanh55 · Answer

A = 1 + 2^1 + 2^2 + 2^3 + ..... + 2^98   A = ( 1 + 2^1 + 2^2 ) + ( 2^3 + 2^4 + 2^5 ) + .... + ( 2^96 + 2^97 + 2^98 )   A = ( 1 + 2^1 + 2^2 ) . 1 + ( 1 + 2^1 + 2^2 ) . 2^3 + .... + ( 1 + 2^1 + 2^2 ) . 2^96   A = ( 1 + 2^1 + 2^2 ) . ( 1 + 2^3 + .... + 2^96 )   A = ( 1 + 2 + 4 ) . ( 1 + 2^3 + .... + 2^96 )   A = 7 . ( 1 + 2^3 + .... + 2^96 ) vdots 7 ( Điều phải chứng minh )