Đáp án:
Giải thích các bước giải:
Ta có: A = $2^{0}$ + $2^{1}$ + $2^{2}$ + $2^{3}$ + $2^{4}$ +...+ $2^{95}$ + $2^{96}$ + $2^{97}$ + $2^{98}$ + $2^{99}$
=> A = ($2^{0}$ + $2^{1}$ + $2^{2}$ + $2^{3}$ + $2^{4}$) +...+ ($2^{95}$ + $2^{96}$ + $2^{97}$ + $2^{98}$ + $2^{99}$)
=> A = (1 + $2^{1}$ + $2^{2}$ + $2^{3}$ + $2^{4}$) +...+ ($2^{95}$.1 + $2^{95}$.2 + $2^{95}$.$2^{2}$ + $2^{95}$.$2^{3}$ + $2^{95}$.$2^{4}$)
=> A = 1.(1 + $2^{1}$ + $2^{2}$ + $2^{3}$ + $2^{4}$) +...+ $2^{95}$.(1 + $2^{1}$ + $2^{2}$ + $2^{3}$ + $2^{4}$)
=> A = (1 +...+ $2^{95}$).(1 + $2^{1}$ + $2^{2}$ + $2^{3}$ + $2^{4}$)
=> A = (1 +...+ $2^{95}$).31 chia hết cho 31
Vậy A chia hết cho 31 (điều phải chứng mình)
