Đáp án:
a) A chia hết cho 2,5, A không chia hết cho 3.
b) \(U\left( { - 10} \right) = \left\{ { \pm 1; \pm 2; \pm ; \pm 10} \right\}\)
Giải thích các bước giải:
\(\begin{array}{l}
A = 1 - 2 + 3 - 4 + 5 - 6 + ... + 19 - 20\\
A = \left( {1 + 3 + 5 + ... + 19} \right) - \left( {2 + 4 + 6 + ... + 20} \right)\\
A = {A_1} - {A_2}\\
{A_1} = 1 + 3 + 5 + ... + 19\\
SSH = \left( {19 - 1} \right):2 + 1 = 10\\
Tong = \left( {1 + 19} \right).10:2 = 100\\
{A_2} = 2 + 4 + 6 + ... + 20\\
SSH = \left( {20 - 2} \right):2 + 1 = 10\\
Tong = \left( {2 + 20} \right).10:2 = 110\\
\Rightarrow A = 100 - 110 = - 10.\\
a){\mkern 1mu} {\mkern 1mu} A{\mkern 1mu} {\mkern 1mu} \vdots {\mkern 1mu} {\mkern 1mu} 2,{\mkern 1mu} {\mkern 1mu} A{\mkern 1mu} {\mkern 1mu} \,khong\,\,chia\,\,het\,\,cho\,\,3,{\mkern 1mu} {\mkern 1mu} A{\mkern 1mu} {\mkern 1mu} \vdots {\mkern 1mu} {\mkern 1mu} 5\\
b){\mkern 1mu} {\mkern 1mu} - 10 = - 2. - 5\\
\Rightarrow U\left( { - 10} \right) = \left\{ { \pm 1; \pm 2; \pm ; \pm 10} \right\}
\end{array}\)
