1 . cho dãy A= 1+4+4^2+4^3+...+4^4 Chứng Minh Rằng : a) A không chia hết cho 5 b) A không chia hết cho 7

$\text{Bài 1 :}$

$\text{a) Ta có : A = 1 + 4 + $4^{2}$  + $4^{3}$  +  $4^{4}$ }$

$\text{A = ( 1 + 4 ) + ( $4^{2}$  + $4^{3}$ ) +  $4^{4}$ }$

$\text{A = 5 + 5 × $4^{2}$ +  $4^{4}$ }$

$\text{A = 5 × ( 1 + $4^{2}$ ) +  $4^{4}$ }$

$\text{Do 5 $\vdots$ 5 nên 5 × ( 1 + $4^{2}$ ) ⇒ 5 × ( 1 + $4^{2}$ ) +  $4^{4}$ $\not\vdots$ 5 nên}$ $\text{A $\not\vdots$ 5 }$

$\text{Vậy A $\not\vdots$ 5 }$

$\text{b) A = 1 + 4 + $4^{2}$  + $4^{3}$  +  $4^{4}$ }$

$\text{A = ( 1 + 4 + $4^{2}$  ) + ( $4^{3}$  +  $4^{4}$ ) }$

$\text{A = 21 + $4^{3}$  × 5 }$

$\text{A = 7 × 3 + $4^{3}$  × 5 }$

$\text{Do 7 $\vdots$ 7 nên 7 × 3 $\vdots$ 7 ⇒ 7 × 3 + $4^{3}$  × 5 $\not\vdots$ 7 nên A}$ $\text{$\not\vdots$ 7}$

$\text{Vậy  A $\not\vdots$ 7}$