Question

Chứng minh A 2¹ +2²+2³+2⁴ ...2^{2010 chia hết cho 3,7}

 

Answer 1

A=2+2^2+2^3+2^4+...+2^2010

=(2+2^2)+(2^3+2^4)+...+(2^2009+2^2010)

=2(1+2)+2^3(1+2)+...+2^2009(1+2)

3(2+2^3+...+2^2009) chia hết cho 3

 

A=2+2^2+2^3+2^4+...+2^2010

=(2+2^2+2^3)+(2^4+2^5+2^6)+...+(2^2008+2^2009+2^2010)

=2(1+2+2^2)+2^4(1+2+2^2)+...+2^2008(1+2+2^2)

=7(2+2^4+...+2^2008) chia hết cho 7