A = 2 + $2^{2}$ + $2^{3}$ + ... + $2^{98}$
a) Ta có:
A = 2 + $2^{2}$ + $2^{3}$ + ... + $2^{98}$
A = 2 . (1 + 2 + $2^{2}$ + $2^{3}$ + ... + $2^{97}$)
Vậy A $\vdots$ 2
b) Ta có:
A = 2 + $2^{2}$ + $2^{3}$ + ... + $2^{98}$
A = (2 + $2^{2}$) + ($2^{3}$ + $2^{4}$) + ... + ($2^{97}$ + $2^{98}$)
A = (2 + $2^{2}$) + $2^{2}$ . (2 + $2^{2}$) + $2^{4}$ . (2 + $2^{2}$) + ... + $2^{96}$ . (2 + $2^{2}$)
A = 6 + $2^{2}$ . 6 + $2^{4}$ . 6 + ... + $2^{96}$ . 6
A = 6 . (1 + $2^{2}$ + $2^{4}$ + $2^{6}$ + ... + $2^{96}$)
Vậy A $\vdots$ 3
c) Ta có:
A = 2 + $2^{2}$ + $2^{3}$ + ... + $2^{98}$
A = (2 + $2^{2}$) + ($2^{3}$ + $2^{4}$ + $2^{5}$) + ... + ($2^{96}$ + $2^{97}$ + $2^{98}$)
A = 6 + $2^{2}$ . (2 + $2^{2}$ + $2^{3}$) + $2^{5}$ . (2 + $2^{2}$ + $2^{3}$) + ... + $2^{95}$ . (2 + $2^{2}$ + $2^{3}$)
A = 6 + $2^{2}$ . 14 + $2^{5}$ . 14 + ... + $2^{95}$ . 14
A = 6 + 14 . ($2^{2}$ + $2^{5}$ + $2^{8}$ + ... + $2^{95}$)
A = 6 + 2 . 7 . ($2^{2}$ + $2^{5}$ + $2^{8}$ + ... + $2^{95}$)
Vì 2 . 7 . ($2^{2}$ + $2^{5}$ + $2^{8}$ + ... + $2^{95}$) $\vdots$ 7 nên 6 + 2 . 7 . ($2^{2}$ + $2^{5}$ + $2^{8}$ + ... + $2^{95}$) chia 7 dư 6
Vậy A chia 7 dư 6
