Toán Lớp 6: Cho A = 2+2 mũ 2+2 mũ 3+-..+2 mũ 60 . Chứng tỏ rằng A chia hết cho 3,5,7

Question

Toán Lớp 6:  Cho A = 2+2 mũ 2+2 mũ 3+......+2 mũ 60 . Chứng tỏ rằng A chia hết cho 3,5,7

haianhtu97 · Answer

A=2+2&sup2;+2&sup3;+...+2 mũ 60   A=(2+2&sup2;+2&sup3;)+...+(2 mũ 58 + 2 mũ 59 + 2 mũ 60)   A=2&times;(1+2+2&sup2;)+...+2 mũ 58&times;(1+2+2&sup2;)   A=2&times;7+...+2 mũ 58&times;7   A=7&times;(2+...+2 mũ 58)   Vậy A chia hết cho 3,5,7

lanhuongthu · Answer

A=2+2^2+2^3+...+2^60   =2(1+2)+2^2(1+2)+...+2^59(1+2)   =3(2+2^2+...+2^59)   V&igrave; 3 vdots3    =>3(2+2^2+...+2^59) vdots3   =>A vdots3   _________________________________________   A=2+2^2+2^3+...+2^60   =2(1+2+2^2+2^3)+...+2^57(1+2+2^2+2^3)   =15(2+...+2^57)   V&igrave; 15 vdots5   =>15(2+...+2^57) vdots5   =>A vdots5   _________________________________________   A=2+2^2+2^3+...+2^60   =2(1+2+2^2)+2^4+(1+2+2^2)+...+2^58(1+2+2^2)   =7(2+2^4+...+2^58)   V&igrave; 7 vdots7   =>7(2+2^4+...+2^58) vdots7   =>A vdots7