Question

giúp mik với ạ

Answer 1

Bài 1:

$A=4+4^2+4^3+...+4^{23}+4^{24}$

$=(4+4^2)+(4^3+4^4)+....+(4^{23}+4^{24})$

$=4(1+4)+4^3(1+4)+....+4^{23}(1+4)$

$=4.5+4^3.5+...+4^{23}.5$

$=4.5(1+4^2+...+4^{22})=20(1+4^2+...+4^{22})\vdots 20$

Ta có đpcm

Answer 2

Bài 2:
$A=1+2+2^2+2^3+2^4+....+2^{99}+2^{100}$

$=1+(2+2^2)+(2^3+2^4)+...+(2^{99}+2^{100})$
$=1+2(1+2)+2^3(1+2)+...+2^{99}(1+2)$
$=1+2.3+2^3.3+...+2^{99}.3$
$=1+3(2+2^3+...+2^{99})$

Vậy $A$ chia $3$ dư $1$