Đáp án:
Giải thích các bước giải:
A = $2^{0}$ + $2^{1}$ + $2^{2}$ + $2^{3}$ + $2^{4}$ + $2^{5}$ + ..... + $2^{95}$ + $2^{96}$ + $2^{97}$
→ A = ( $2^{0}$ + $2^{1}$ + $2^{2}$ ) + ( $2^{3}$ + $2^{4}$ + $2^{5}$ ) + ..... + ( $2^{95}$ + $2^{96}$ + $2^{97}$ )
→ A = $2^{0}$ . ( $2^{0}$ + $2^{1}$ + $2^{2}$ ) + $2^{3}$ . ( $2^{0}$ + $2^{1}$ + $2^{2}$ ) + ..... + $2^{95}$ . ( $2^{0}$ + $2^{1}$ + $2^{2}$ )
→ A = $2^{0}$ . 7 + $2^{3}$ . 7 + ..... + $2^{95}$ . 7
→ A = 7 . ( $2^{0}$ + $2^{3}$ + ..... + $2^{95}$ )
Vì 7 . ( $2^{0}$ + $2^{3}$ + ..... + $2^{95}$ ) chia hết cho 7
→ A chia hết cho 7 ( Điều phải chứng minh )
