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\(\Rightarrow x\in\left\{-9;-8;...;16\right\}\)
Tổng là: \(\dfrac{\left(16-9\right)\left(\dfrac{16+9}{1}+1\right)}{2}=91\)
1) \(-4< x< 3\)
\(\Rightarrow x\in\left\{-3;-2;-1;0;1;2\right\}\)
Tổng:
\(\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2\)
\(=\left(-2+2\right)+\left(-1+1\right)+0-3\)
\(=-3\)
2) \(-5< x< 5\)
\(\Rightarrow x\in\left\{-4;-3;-2;-1;0;1;2;3;4\right\}\)
Tổng:
\(\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+3\)
\(=\left(-4+4\right)+\left(-3+3\right)+\left(-2+2\right)+\left(-1+1\right)+0\)
\(=0\)
3) \(-10< x< 6\)
\(\Rightarrow x\in\left\{-9;-8;-7;-6;-5;-4;-3;-2;-1;0;1;2;3;4;5\right\}\)
Tổng:
\(\left(-9\right)+\left(-8\right)+\left(-7\right)++\left(-6\right)+\left(-5\right)+\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+4+5\)
\(=-24\)
4) \(-6< x< 5\)
\(\Rightarrow x\in\left\{-5;-4;-3;-2;-1;0;1;2;3;4\right\}\)
Tổng:
\(\left(-5\right)+\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+4\)
\(=\left(-4+4\right)+\left(-3+3\right)+\left(-2+2\right)+\left(-1+1\right)+0-5\)
\(=-5\)
5) \(-5< x< 2\)
\(\Rightarrow x\in\left\{-4;-3;-2;-1;0;1\right\}\)
Tổng:
\(\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1\)
\(=\left(-1+1\right)+0+\left(-4-3-2\right)\)
\(=-6\)
x⊂{-9;-8;-7;-6;-5;-4;-3;-2;-1;0;1;2;3;4;5;6;7;8;9;10;11}
Tổng của các số nguyên x là bằng (-9)+(-8)+(-7)+(-6)+(-5)+(-4)+(-3)+(-2)+(-1)+0+1+2+3+4+5+6+7+8+9+10+11=21
Lời giải:
$\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{n(n+1)}=\frac{2022}{2023}$
$\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{n(n+1)}=\frac{2022}{2023}$
$2[\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{n(n+1)}]=\frac{2022}{2023}$
$2[\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{n(n+1)}]=\frac{2022}{2023}$
$2(\frac{1}{2}-\frac{1}{n+1})=\frac{2022}{2023}$
$1-\frac{2}{n+1}=1-\frac{1}{2023}$
$\Rightarrow \frac{2}{n+1}=\frac{1}{2023}$
$\Rightarrow n+1=2.2023=4046$
$\Rightarrow n=4045$
Có ( -10 ) \(⋮\)( n - 3 ) \(\Rightarrow\)( n - 3 ) \(\in\)Ư ( -10 ) Ư ( -10 ) = { 1; -1 ; 2; -2; 5;-5;10;-10}
Nếu n - 3 = 1 thì : n = 4
Nếu n - 3 = -1 thì : n = 2
Nếu n - 3 = 2 thì : n = 5
Nếu n - 3 = - 2 thì : n = 1
Nếu n - 3 = 5 thì : n = 8
Nếu n - 3 = -5 thì : n = -2
Nếu n - 3 = 10 thì : n = 13
Nếu n - 3 = -10 thì : n = -7
Vậy n \(\in\){ 4;2;5;1;8;-2;13;-7 }
\(\Leftrightarrow\left(x+3\right)^3:3=-9\)
=>x+3=-3
hay x=-6