Question

arata ca 2+2^2+2^3+....+2^2016 este divizibil cu 30

Answer 1

2+2^2+2^3+....+2^2016 =
2016 :4=504   deci putem grupa cate 4
=(2+2^2+2^3+2^4)+....+(2^13+2^14+2^15+2^2016) =
=(2+4+8+16)+....+2^12(2+2^2+2^3+2^4)=
=30+....+2^12×(2+4+8+16)=
=30+....+2^12×30=
=30×(1+...+2^12)  deci divizibil cu 30

Answer 2

2+2^2+2^3+....+2^2016 =
2016 :4=504   
(2+2^2+2^3+2^4)+....+(2^13+2^14+2^15+2^2016) =
=(2+4+8+16)+....+2^12(2+2^2+2^3+2^4)=
=30+....+2^12×(2+4+8+16)=
=30+....+2^12×30=
=30×(1+...+2^12)