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ta có :\(\frac{n\left(n+1\right)}{2}\)= 3570
=> n ( n+1 ) = 7140
=> 7140 = 84 x 85
=> n = 84
1 + 2 + 3 + 4 + ... + x = 3570
[ ( x - 1 ) : 1 + 1 ] . ( x + 1 ) : 2 = 3570
[ x - 1 + 1 ] . ( x + 1 ) : 2 = 3570
x . ( x + 1 ) : 2 = 3570
x . ( x + 1 ) = 3570 . 2
x . ( x + 1 ) = 7140
x . ( x + 1 ) = 84 . 85
=> x = 84
A) \(x-\dfrac{2}{3}=\dfrac{4}{5}\\ x=\dfrac{4}{5}+\dfrac{2}{3}\)
\(x=\dfrac{22}{15}\)
b)\(\dfrac{7}{9}-x=\dfrac{1}{3}\\ x=\dfrac{7}{9}-\dfrac{1}{3}\\ x=\dfrac{4}{9}\)
C)\(x:\dfrac{2}{3}=\dfrac{9}{8}\\ x=\dfrac{9}{8}x\dfrac{2}{3}\\ x=\dfrac{3}{4}\)
\(\left(x+9\right)+\left(x-8\right)+\left(x+7\right)+\left(x-6\right)+\left(x+5\right)+\left(x-4\right)+\left(x+3\right)+\left(x-2\right)+\left(x+1\right)=95.9\\ =>x+9+x-8+x+7+x-6+x+5+x-4+x+3+x-2+x+1=855\\ =>\left(x+x+x+x+x+x+x+x+x\right)+\left(9-8+7-6+5-4+3-2+1\right)=855\\ =>9x+5=855\\ =>9x=855-5\\ =>9x=850\\ =>x=\dfrac{850}{9}\)
\(\left(x+9\right)+\left(x-8\right)+...+\left(x-2\right)+\left(x+1\right)\)
\(=x+9+x-8+...+x-2+x+1\)
\(=\left(x+9+x-8\right)+...+\left(x+5\right)+...+\left(x-2+x+1\right)\)
(Ta gộp 4 số vào 1 tổng, riêng (x+5) là ta giữ nguyên)
\(=\left(2x-1\right)+...+\left(x+5\right)+...+\left(2x-1\right)\)
\(=4\left(2x-1\right)+\left(x+5\right)\)
\(=8x-4+x-5\)
\(=9x-9\) (1)
Từ bài toán trên, ta có:
\(\left(x+9\right)+\left(x-8\right)+...+\left(x-2\right)+\left(x+1\right)=95,9\)
Từ (1)
\(\Leftrightarrow9x-9=95,9\)
\(9x=95,9-9\)
\(x=86,9:9\)
\(x=9,6\left(5\right)\)
1. \(1\frac{1}{5}x1\frac{1}{6}x1\frac{1}{7}x...x1\frac{1}{2006}\)
\(=\frac{6}{5}x\frac{7}{6}x\frac{8}{7}x...x\frac{2007}{2006}\)
\(=\frac{6x7x8x...x2007}{5x6x7x...x2006}\)
\(=\frac{2007}{5}.\)
2. Câu này đề chắc chắn sai.
3.\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x...x\left(1-\frac{1}{2600}\right)\)
\(=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x...x\frac{2599}{2600}\)
\(=\frac{1x2x3x...x2599}{2x3x4x...x2600}\)
\(=\frac{1}{2006}.\)
3(x+2)=12(6-x)+1
=> 3x +6 = 72 -12x +1
=> 3x + 6 -72 +12x -1 =0
=> 15x -67 =0
=> 15x = 67
=> x = 67/15
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(x+x+x+x+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=1\)
\(\left(x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=1\)
\(4\times x+\frac{15}{16}=1\)
\(4\times x=1-\frac{15}{16}\)
\(4\times x=\frac{1}{16}\)
\(x=\frac{1}{16}:4\)
\(x=\frac{1}{64}\)
( x+1/2) +(1/4) + ( x + 1/8 ) + ( x + 1/6 ) = 1
x * 4 + 1/2 + 1/4 + 1/8 + 1/6 = 1
x * 4 + 1/2 + 1/4 + 1/8 = 1 - 1/6
x * 4 + 1/2 + 1/4 + 1/8 = 5/6
x * 4 + 1/2 + 1/4 = 5/6 -1/8
x * 4 + 1/2 + 1/4 = 17/24
x * 4 + 1/2 = 17/24 - 1/4
x * 4 + 1/2 = 11/24
x * 4 = 11/24 - 1/2
x * 4 = -1/24
x = -1/24 : 4
x = -1/96