Question

Fie x=3¹+3²+3³+...+3¹².Aratati că :
a)x divizibil cu 3
b)x divizibil cu 4
Va rog urgent....dau Coroana !

Answer 1

$x=3+3^2+3^3+...+3^{12}$
$a)~x=3(1+3+3^2+...+3^{11})~\vdots~3$
$b)~3+3^2=3+9=12=3\cdot4$
$x=(3+3^2)+(3^3+3^4)+...+(3^{11}+3^{12})$
$x=(3+3^2)+3^2(3+3^2)+...+3^{10}(3+3^2)$
$x=(1+3^2+...+3^{10})(3+3^2)$
$x=(1+3^2+...+3^{10})\cdot12~\vdots~4$