Toán Lớp 6: cho A= 2 + 2 mũ 2 + 2 mũ 3 + -.+ 2 mũ 20 chứng minh rằng a) A chia hết cho 2 b) A chia hết cho 3 c) A chia hết cho 5

Question

Toán Lớp 6:  cho A= 2 + 2 mũ 2 + 2 mũ 3 + .....+ 2 mũ 20 chứng minh rằng a) A chia hết cho 2 b) A chia hết cho 3 c) A chia hết cho 5

kimlien · Answer

a)A=2+2^2+2^3+...+2^20   A=2(1+2+2^2+...+2^19)   V&igrave; 2 vdots2   =>2(1+2+2^2+...+2^19) vdots2 hay A vdots2   b)A=2+2^2+2^3+...+2^20   A=(2+2^2)+(2^3+2^4)...+(2^19+2^20)   A=2(1+2)+2^3(1+2)+...+2^19(1+2)   A=2.3+2^3 .3+...+2^19 .3   A=3(2+2^3+...+2^19)   V&igrave; 3 vdots3   =>3(2+2^3+...+2^19) vdots3 hay A vdots3   c)A=2+2^2+2^3+...+2^20   A=(2+2^2+2^3+2^4)+...+(2^17+2^18+2^19+2^20)   A=2(1+2+2^2+2^3)+...+2^17(1+2+2^2+2^3)   A=2.15+...+2^17 .15   A=15(2+...+2^17)   V&igrave; 15 vdots5   =>15(2+...+2^17) vdots5 hay A vdots5

landinhngoc97 · Answer

a + b + c ) Ta c&oacute; : A = 2 + 2^2 + 2^3 + .... + 2^20   A = ( 2 + 2^2 + 2^3 + 2^4 ) + .... + ( 2^17 + 2^18 + 2^19 + 2^20 )   A = 1 . ( 2 + 2^2 + 2^3 + 2^4 ) + .... + 2^16 . ( 2 + 2^2 + 2^3 + 2^4 )   A = ( 2 + 2^2 + 2^3 + 2^4 ) . ( 1 + .... + 2^16 )   A = ( 2 + 4 + 8 + 16 ) . ( 1 + .... + 2^16 )   A = 30 . ( 1 + .... + 2^16 ) vdots 30   M&agrave; 30 vdots 2 , 30 vdots 3 , 30 vdots 5   &rArr; A vdots 2 ,  A vdots 3 , A vdots 5 ( Điều phải chứng minh )   ** T&iacute;nh chất :   a vdots b ; b vdots c , b vdots d &rArr; a vdots c , a vdots d