Question

Chứng minh rằng:  A = 3+3^2+3^3+............+3^60 chia hết cho 13

Answer 1

ta co :(3+3^2+3^3)+.......+(3^58+3^59+3^60)

=3(1+3+3^2)+.....+3^58(1+3+3^2)

=3.13+.........+3^58.13chia hết cho 13

Answer 2

A=3+3^2+3^3+....+3^60

=(3+3^2+3^3)+(3^4+3^5+3^6)+...+(3^58+3^59+3^60)

=(3+9+27)+(3^3.3+3^3.9+3^3.27)+...+(3^57.3+3^57.9+3^57.27)

=39+3^3.(3+9+27)+....+3^57.(3+9+27)

=39+3^3.39+....+3^57.39

vì 39:13 nên=>chia hết cho 13