Question

Ai giải chi tiết mik sẽ theo dõi,cần gấp

Answer 1

1.

$A=2+2^2+2^3+2^4+...+2^{10}$
$=(2+2^2+2^3+2^4)+(2^5+2^6+2^7+2^8)+2^9+2^{10}$

$=2(1+2+2^2+2^3)+2^5(1+2+2^2+2^3)+2^9(1+2)$

$=15(2+2^5)+3.2^9$

Ta thấy $15(2+2^5)\vdots 5$ còn $3.2^9\not\vdots 5$

$\Rightarrow A\not\vdots 5$

Answer 2

Bài 2:

$B=2+2^2+2^3+2^4+...+2^{99}+2^{100}$

$=(2+2^2)+(2^3+2^4)+(2^5+2^6)+...+(2^{99}+2^{100})$

$=2(1+2)+2^3(1+2)+2^5(1+2)+...+2^{99}(1+2)$
$=(1+2)(2+2^3+2^5+...+2^{99})$

$=3(2+2^3+2^5+...+2^{99})\vdots 3$