A = 2 + 2 ² + 2 ³ + ... + $2^{100}$
= ( 2 + 2 ² + 2 ³+ $2^{4}$ ) + ... + ( + $2^{97}$ + $2^{98}$ + $2^{99}$ + $2^{100}$
= 2 . ( 2 + 2 ² + 2 ³+ $2^{4}$ ) + ... + $2^{97}$ . ( 2 + 2 ² + 2 ³+ $2^{4}$ )
= 2 . 30 + . . . + $2^{97}$ . 30
= 30 + ( 2 + . . . + $2^{97}$ )
Vây A chia hết cho 30