a, A = 2 + 2² + 2³+ ...+ 20²⁰
A = 1 . 2 + 2 . 2 + 2 . 2² + . . . + 2 . $2^{19}$
A = 2 ( 1 + 2 + 2² + . . . + $2^{19}$ )
Vì 2 chia hết cho 2 ⇒ A chia hết cho 2 ( đpcm )
b, A = 2 + 2² + 2³+ ...+ 20²⁰
A = ( 2 + 2² ) + ( 2³+ $2^{4}$ ) + . . . + ( $2^{19}$ + 20²⁰ )
A = 2 ( 1 + 2 ) + 2³ ( 1 + 2 ) + . . . + $2^{19}$ ( 1 + 2 )
A = 3 . 2 + 3 . 2³ + . . . + 3 . $2^{19}$
A = 3 ( 2 + 2³ + . . . + $2^{19}$ )
Vì 3 chia hết cho 3 ⇒ A chia hết cho 3 ( đpcm )
c, A = 2 + 2² + 2³+ ...+ 20²⁰
A = [( 2 + 2³ ) + ( $2^{5}$ + $2^{7}$ ) + . . . + ( $2^{17}$ + $2^{19}$ )] + [( 2² + $2^{4}$ ) + ( $2^{6}$ + $2^{8}$ ) + . . . + ( $2^{18}$ + $2^{20}$ )]
A = [2 ( 1 + 2² ) +$2^{5}$ ( 1 + 2² ) + . . . + $2^{17}$ ( 1 + 2² ) ] + [ 2² ( 1 + 2² ) + $2^{6}$ ( 1 + 2² ) + . . . + $2^{18}$ ( 1 + 2² )]
A = 2 . 5 + $2^{5}$ . 5 + . . . + $2^{17}$ . 5 + 2² . 5 + $2^{6}$ . 5 + . . . + $2^{18}$ . 5
A = 5 ( 2 + $2^{5}$ + . . . + $2^{17}$ + 2² + $2^{6}$ + . . . + $2^{18}$ )
Vì 5 chia hết cho 5 ⇒ A chia hết cho 5 ( đpcm )
