Bài 3
a)vì 5a +8b chia hết cho 9
=> 2(5a+8b) chia hết cho 9
=> 10a +16b chia hết cho 9
=> 10a+16b-9b chia hết cho 9
=> 10a +7b chia hết cho 9(đpcm)
b) vì 5a+8b ⋮ 9
=> 2(5a+8b)⋮9
=>16b+10a⋮9
=> 16b+10a-9a ⋮ 9
=>16b+a ⋮ 9(đpcm)
Bài 4:
a)Ta có: S=2-$2^{2}$ + $2^{3}$ -...+$2^{99}$ -$2^{100}$
=> 2S= $2^{2}$ -$2^{3}$ +...+$2^{100}$ -$2^{101}$
=> 2S+S=(2-$2^{2}$ + $2^{3}$ -...+$2^{99}$ -$2^{100}$ )+($2^{2}$ -$2^{3}$ +...+$2^{100}$ -$2^{101}$ )
=> 3S=2-$2^{101}$
=> S=$\frac{2-2^{101}}{3}$
b)Ta có: S=2-$2^{2}$ + $2^{3}$ -...+$2^{99}$ -$2^{100}$
=> S=(2-$2^{2}$ + $2^{3}$ -$2^{4}$)+...+($2^{97}$-$2^{98}$+$2^{99}$ -$2^{100}$)
=-10+...+$2^{96}$(2-$2^{2}$ + $2^{3}$ -$2^{4}$)
=(-10)(1+$2^{4}$+...+$2^{96}$) chia hết cho -5
CHO HAY NHẤT NHA
