LG a
\(\, -4 < x < 5\)
\(- 4 < x < 5\)
Suy ra \( x \in \left\{ { - 3; - 2; - 1;0;1;2;3;4} \right\}\)
Ta có: \((-3)+(-2) +(-1) + 0 + 1 + 2 + 3\)\( + 4\)
\(=\left[ {\left( { - 3} \right) + 3} \right] + \left[ {\left( { - 2} \right) + 2} \right]\) \( + \left[ {\left( { - 1} \right) + 1} \right] \)\(+ 0 + 4\)
\(= 0 + 0 + 0 + 0 + 4 = 4\)
LG b
\(b)\, -7 < x < 5\)
\( -7 < x < 5\)
Suy ra \(x \in \left\{ { - 6; - 5; - 4; ...;\,2;\,3;\,4} \right\}\)
Ta có \((-6)+(-5)+(-4)+(-3)\) \(+(-2)+(-1)\) \( + 0 + 1 +2 + 3 + 4\)
\(=\left[ {\left( { - 6} \right) + \left( { - 5} \right)} \right] + \left[ {\left( { - 4} \right) + 4} \right] \) \(+ \left[ {\left( { - 3} \right) + 3} \right] \) \(+\left[ {\left( 2 \right) + 2} \right]\)\( + \left[ {\left( { - 1} \right) + 1} \right] + 0\)
\(= (-11) + 0 +0 + 0 + 0 + 0 = -11\)
LG c
\(\, -19 < x < 20\)
\({\rm{ }} - 19{\rm{ }} < {\rm{ }}x{\rm{ }} < {\rm{ }}20 \)
Suy ra \( x \in \left\{ { - 18; - 17; - 16;...;17;18;19} \right\}\)
Ta có: \((-18) + (-17) +(-16)\)\( + … +0\) \( + … + 17 + 18+ 19\)
\(=\left[ {\left( { - 18} \right) + 18} \right] + \left[ {\left( { - 17} \right) + 17} \right] + ... +\)
\(\left[ {\left( { - 1} \right) + 1} \right] + 0 + 19\)
\(= 0+ 19 =19\)
