$2$ + $2^{2}$ +$2^{3}$ +$2^{4}$ $+....+$ $2^{60}$
=( $2$ + $2^{2}$ + $2^{3}$ )$+....+$( $2^{58}$ + $2^{59}$ + $2^{60}$ )
=($2.1$ + $2.2$ + $2^{2} .2$) $+...+$ ( $2^{58}.1$ + $2^{58}.2$ +$2^{58}$.$2^{2}$)
=$2$ .($1$+$2$+$2^{2}$) $+...+$ $2^{58}$ . ($1$ +$2$ +$2^{2}$)
=$2$ . $7$ $+...+$ $2^{58}$ . $7$
=$7$ . ($2$ $+..+$ $2^{58}$) $ chia hết cho 7(vì 7 chia hết cho 7)
⇒ $A$ $chia$ $hết$ $cho$ $7$
$⇒Dpcm (điều phải chứng minh)$
$cho$ $mk$ $xin$ $hay$ $nhất$ $nha$
