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Tính
Aleft(dfrac{1}{3}-1right)left(dfrac{1}{6}-1right)left(dfrac{1}{10}-1right)left(dfrac{1}{15}-1right)left(dfrac{1}{21}-1right)left(dfrac{1}{28}-1right)left(dfrac{1}{36}-1right)
Bleft(1-dfrac{1}{2^2}right)left(1-dfrac{1}{3^2}right)........left(1-dfrac{1}{10^2}right)
C1+dfrac{1}{2}+dfrac{1}{2^2}+dfrac{1}{2^3}+..........+dfrac{1}{2^{2016}}
Giúp mk nha!Cảm ơn rất nhìu!
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Tính
A=\(\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{6}-1\right)\left(\dfrac{1}{10}-1\right)\left(\dfrac{1}{15}-1\right)\left(\dfrac{1}{21}-1\right)\left(\dfrac{1}{28}-1\right)\left(\dfrac{1}{36}-1\right)\)
B=\(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)........\left(1-\dfrac{1}{10^2}\right)\)
C=\(1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+..........+\dfrac{1}{2^{2016}}\)
Giúp mk nha!Cảm ơn rất nhìu!
Tính giá trị biểu thức :
\(\dfrac{1}{2}-\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}\right)-\left(\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{4}{5}\right)+\left(\dfrac{1}{6}+\dfrac{2}{6}+\dfrac{3}{6}+\dfrac{4}{6}+\dfrac{5}{6}\right)-\left(\dfrac{1}{7}+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{4}{7}+\dfrac{5}{7}+\dfrac{6}{7}\right)+...+\left(100+...+\dfrac{99}{100}\right)\)
a) A = \(\left(\dfrac{1}{1009}+\dfrac{1}{1010}+...+\dfrac{1}{2015}+\dfrac{1}{2016}\right):\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)
b) B = \(\dfrac{5x^2+3y^2}{10x^2-3y^2}\) biết \(\dfrac{x}{3}=\dfrac{y}{5}\)
tính:
dfrac{2}{5}xdfrac{1}{3}-dfrac{2}{15}:dfrac{1}{5}+dfrac{3}{5}xdfrac{1}{3}
2)left(3dfrac{1}{3}+2,5right):left(3dfrac{1}{6}-4dfrac{1}{5}right)-dfrac{11}{31}
3)left[6+left(dfrac{1}{2^{ }}right)^3-left|-dfrac{1}{2}right|right]:dfrac{3}{12}
4)dfrac{18}{37}+dfrac{8}{24}+dfrac{19}{37}-1dfrac{23}{24}+dfrac{2}{3}
5) left(-2right)^3xleft(dfrac{3}{4}-0,25right):left(2dfrac{1}{4}-1dfrac{1}{6}right)
6)left(dfrac{2}{5}right)^2+5dfrac{1}{2}xleft(45-2right)+dfrac{23}{-4}
7)dfrac{4}{9}-19dfrac{1}{3}-...
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tính:
\(\dfrac{2}{5}x\dfrac{1}{3}-\dfrac{2}{15}:\dfrac{1}{5}+\dfrac{3}{5}x\dfrac{1}{3}\)
2)\(\left(3\dfrac{1}{3}+2,5\right):\left(3\dfrac{1}{6}-4\dfrac{1}{5}\right)-\dfrac{11}{31}\)
3)\(\left[6+\left(\dfrac{1}{2^{ }}\right)^3-\left|-\dfrac{1}{2}\right|\right]:\dfrac{3}{12}\)
4)\(\dfrac{18}{37}+\dfrac{8}{24}+\dfrac{19}{37}-1\dfrac{23}{24}+\dfrac{2}{3}\)
5) \(\left(-2\right)^3x\left(\dfrac{3}{4}-0,25\right):\left(2\dfrac{1}{4}-1\dfrac{1}{6}\right)\)
6)\(\left(\dfrac{2}{5}\right)^2+5\dfrac{1}{2}x\left(45-2\right)+\dfrac{23}{-4}\)
7)\(\dfrac{4}{9}-19\dfrac{1}{3}-\dfrac{4}{9}x39\dfrac{1}{3}\)
8)\(\left(-\dfrac{1}{2}\right)^2:\dfrac{1}{4}-2x\left(-\dfrac{1}{2}\right)^2\)
9)\(125\%x\left(-\dfrac{1}{2}\right)^3:\left(1\dfrac{5}{16}-1,5\right)+2008^0\)
giúp mình nha mai mình học rùi 
1: rút gọn rồi tính
left(-dfrac{72}{40}-dfrac{144}{60}-2dfrac{1}{3}right) : left(dfrac{45}{100}-dfrac{25}{60}+-dfrac{75}{25}right)
2: tìm x: 3cdotleft(4-xright)+left(x+2right)cdotleft(1+2xright)7cdotleft(1+xright)-2xcdotleft(2-xright)
3: tìm x: dfrac{2cdotleft(1+xright)}{3}-dfrac{5cdotleft(2-xright)}{6}1dfrac{1}{3}-dfrac{3cdotleft(2x+3right)}{4}-1dfrac{1}{2}cdotleft(x+1right)
4: cho a 3+3^{2^3}+3^3+3^4+...+3^{360}
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1: rút gọn rồi tính
\(\left(-\dfrac{72}{40}-\dfrac{144}{60}-2\dfrac{1}{3}\right)\) : \(\left(\dfrac{45}{100}-\dfrac{25}{60}+-\dfrac{75}{25}\right)\)
2: tìm x: \(3\cdot\left(4-x\right)+\left(x+2\right)\cdot\left(1+2x\right)=7\cdot\left(1+x\right)-2x\cdot\left(2-x\right)\)
3: tìm x: \(\dfrac{2\cdot\left(1+x\right)}{3}-\dfrac{5\cdot\left(2-x\right)}{6}=1\dfrac{1}{3}-\dfrac{3\cdot\left(2x+3\right)}{4}-1\dfrac{1}{2}\cdot\left(x+1\right)\)
4: cho a= \(3+3^{2^3}+3^3+3^4+...+3^{360}\)
Tính S=\(\left(1-\dfrac{1}{1+2}\right).\left(1-\dfrac{1}{1+2+3}\right).\left(1-\dfrac{1}{1+2+3+4}\right).....\left(1-\dfrac{1}{1+2+...+2014}\right)\)
BT1: Tính
1) \(\dfrac{1}{2}-\text{|}\dfrac{1}{5}-\dfrac{1}{4}\text{|}+\left(-\dfrac{1}{3}\right)^2\)
2) \(\dfrac{1}{3}+\dfrac{4}{3}.\left(\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{-2}{3}\right)^2\)
Chứng minh rằng :
a)dfrac{1}{x}-dfrac{1}{x+a}dfrac{a}{xleft(x+aright)}
b)dfrac{1}{xleft(x+1right)}-dfrac{1}{left(x+1right)left(x+2right)}dfrac{2}{xleft(x+1right)left(x+2right)}
c)dfrac{1}{xleft(x+1right)left(x+2right)}-dfrac{1}{left(x+1right)left(x+2right)left(x+3right)}dfrac{3}{xleft(x+1right)left(x+2right)left(x+3right)}
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Chứng minh rằng :
a)\(\dfrac{1}{x}\)-\(\dfrac{1}{x+a}=\dfrac{a}{x\left(x+a\right)}\)
b)\(\dfrac{1}{x\left(x+1\right)}-\dfrac{1}{\left(x+1\right)\left(x+2\right)}=\dfrac{2}{x\left(x+1\right)\left(x+2\right)}\)
c)\(\dfrac{1}{x\left(x+1\right)\left(x+2\right)}-\dfrac{1}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}=\dfrac{3}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)
- Tính nhanh tổng sau:
\(\left(\dfrac{1}{2}-1\right):\left(\dfrac{1}{3}-1\right):\left(\dfrac{1}{4}-1\right):\left(\dfrac{1}{5}-1\right)...:\left(\dfrac{1}{50}-1\right)\)