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\(\frac{1}{x}+\frac{1}{2.x}+\frac{1}{6x}+\frac{1}{12x}+\frac{1}{30x}\)
= \(\frac{1}{x}\left(1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}\right)\)
= \(\frac{1}{x}\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)
= \(\frac{1}{x}\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
=\(\frac{1}{x}\left(1+1-\frac{1}{6}\right)\)
=\(\frac{1}{x}.\frac{11}{6}\)
=\(\frac{11}{6x}\)
\(\left(x-1\right)+\left(x-2\right)+\left(x-3\right)=30\)
\(\left(x-1\right)+\left(x-2\right)+\left(x-3\right)=3.\left(x-2\right)\)
\(3.\left(x-2\right)=30\)
\(3.x-2.3=30\)
\(3.x-6=30\)
\(3.x\) \(=30+6\)
\(3.x\) \(=36\)
\(x\) \(=36:3\)
\(x\) \(=12\)
Vậy \(x=12\)
A = 1x2 + 2x3 + 3x4 + ……….. + 29 x30
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + ……… + 29x30x3 Ax3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) +………… 29x30x(31-28)
Ax3 = 1x2x3 + 2x3x4 -1x2x3 + 3x4x5 – 2x3x4 +……..+ 29x30x31 – 28x29x30 Ax3 = 29x30x31
A = 29x30x31 : 3
A = 290x31
A = 1x2 + 2x3 + 3x4 + ……….. + 29 x30
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + ……… + 29x30x3
Ax3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) +………… 29x30x(31-28)
Ax3 = 1x2x3 + 2x3x4 -1x2x3 + 3x4x5 – 2x3x4 +……..+ 29x30x31 – 28x29x30
Ax3 = 29x30x31
A = 29x30x31 : 3
A = 290x31
Phần a:
x+(x+1)+(x+2)+....+(x+30)=1240
31 . x + (1 + 2 + 3 + 4 +...+ 29 + 30) = 1240
31 . x + 31.15 = 1240
31 . x = 1240 - 31.15
31 . x = 775
x = 775 : 31
x = 25
Phần b:
1 + 2 + 3 +...+ x = 210
(x + 1) . x : 2=210
x . (x + 1) = 420
x . x + x = 420
x . x = 420 - x
Ta thấy:
20 . 20 = 420 - 20
Vậy x = 20
Chúc bạn học giỏi!
x=20
(x+1)+(x+2)+(x+3)+...+(x+30)=795
(x+x+x+...+x)+(1+2+3+...+30)=795
30x+465=795
30x=795-465
30x=330
x=330:30
x=11
Vậy x=11
(x+1)+(x+2)+(x+3)+.....+(x+30)=795
( x+x+x+....+x)+( 1+2+....+30)=795
30.x +465=795
30.x=795-465
x=330:30
x=11
(X+X+X+X)+(1+2+3+4)=30
(X+X+X+X)+ 10 =30
=>(X+X+X+X) =30-10
(X+ X+ X+X) =20
=> X =20:4
Vậy X = 5
\(\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=585\)
\(x\times30+\left(1+2+...+30\right)=585\)
\(x\times30+465=585\)
\(x\times30=585-465\)
\(x\times30=120\)
\(x=120:30\)
\(x=4\)
(x+1)+(x+2)+...+(x+30)=585
=> (x+x+...+x)+(1+2+..+30)=585
=> 30x+465=585
=> 30x=585-465
=> 30x=120
=> x=120:3
=> x=40