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\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{x\left(x+1\right):2}=\frac{2001}{2003}\)
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\left(x+1\right)}=\frac{2001}{2003}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{x\left(x+1\right)}\right)=\frac{2001}{2003}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{2001}{2003}:2=\frac{2001}{4006}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2001}{4006}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2001}{4006}=\frac{1}{2003}\)
=> x+1 = 2003
=> x = 2003 - 1
=> x = 2002
\(\left(x-1\right)\left(2y+3\right)=1\cdot26=26\cdot1=2\cdot13=13\cdot2\)
Ta co bang sau:
x-1 | 1 | 26 | 2 | 13 | ||||
2y+3 | 26 | 1 | 13 | 2 | ||||
x | 2 | 27 | 3 | 14 | ||||
y | 11.5 (loai) | -1(loai) | 5 | -0.5(loai) |
a) 6x / 2 - 84 / 2 - 72 =201
3x - 42 -72 = 201
3x - 114 =201
3x = 315
x = 105
b)3x -3^4 =6^5 / 6^3
3x - 3^4 = 36
3x - 3 * 3^3 = 36
3*(x-27) = 36
x - 27 = 36 / 3
x - 27 = 12
x = 39
x+(x+1)+(x+2)+(x+3)+.......+(x+30)=1240
\(\Leftrightarrow\left(x+x+x.+...x\right)+\left(1+2+3...+30\right)=1240\)
\(\Rightarrow30x+465=1240\)
\(\Rightarrow30x=1240-465=775\)
\(\Rightarrow30x=775\)
\(V\text{ậy}x=\frac{155}{6}\)
1+2+3+.....+x=210
\(\left(1+x\right).x=210\)
\(\Rightarrow x=14\)
x+(x+1)+(x+2)+...+(x+30)=1240
=>x+x+1+x+2+...+x+30=1240
=>(x+x+x+...+x)+(1+2+...+30)=1240
=>31x+[(30-1):1+1] . (30+1) :2=1240
=>31x+30.31:2=1240
=>31x+15.31=1240
=>31(x+15)=1240
=>x+15=1240:31=40
=>x=40-15=25
1+2+3+...+x=210
=>[(x-1):1+1]. (x+1) : 2= 210
=>x.(x+1):2=210
=>x(x+1)=210.2=420
=>x(x+1)=20.21
=>x=20
Nhiều số lắm bạn ơi! Phải có thêm điều kiện gì chứ nhỉ?
3x+2 + 3x+1 + 3x < 1053
=> 3x+2 + 3x+1 + 3x < 36 + 35 + 34
=> x < 4
=> x thuộc {0; 1; 2; 3}
Vậy...
\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right).5x+6}=\frac{2005}{2006}\)
\(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+....+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)
\(1-\frac{1}{5x+6}=\frac{2005}{2006}\)
\(\frac{1}{5x+6}=1-\frac{2005}{2006}\)
\(\frac{1}{5x+6}=\frac{1}{2006}\)
=>5x+6 = 2006
=>5x = 2000
=>x = 400
\(\left(x-1\right)\left(x+3\right)=6\)
\(\Rightarrow6⋮\left(x-1\right),\left(x+3\right)\)
\(\Rightarrow\left(x-1\right),\left(x+3\right)\inƯ\left(6\right)\)
\(\RightarrowƯ\left(6\right)=\left\{1;2;3;6\right\}\)
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