\(C=\dfrac{2006\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2007}\right)}{\left(1+\dfrac{2005}{2}\right)+\left(1+\dfrac{2004}{3}\right)+...+\left(1+\dfrac{1}{2006}\right)+1}\)
\(=\dfrac{2006\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2007}\right)}{\dfrac{2007}{2}+\dfrac{2007}{3}+...+\dfrac{2007}{2007}}=\dfrac{2006}{2007}\)
Giá trị biểu thức \(A=\dfrac{2008+\dfrac{2007}{2}+\dfrac{2006}{3}+\dfrac{2005}{4}+...+\dfrac{2}{2007}+\dfrac{1}{2008}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+...+\dfrac{1}{2008}+\dfrac{1}{2009}}\) là \(A=........\)
Tính\(P=\dfrac{636363.37-373737.63}{1+2+3+...+2006}\)
Tính giá trị biểu thức :
1. \(A=\dfrac{\dfrac{2}{5}+\dfrac{2}{7}-\dfrac{2}{9}-\dfrac{2}{11}}{\dfrac{4}{5}+\dfrac{4}{7}-\dfrac{4}{9}-\dfrac{4}{11}}\)
2. \(B=\dfrac{1^2}{1\cdot2}\cdot\dfrac{2^2}{2\cdot3}\cdot\dfrac{3^2}{3\cdot4}\cdot\dfrac{4^2}{4\cdot5}\)
3. \(C=\dfrac{2^2}{1\cdot3}\cdot\dfrac{3^2}{2\cdot4}\cdot\dfrac{4^2}{3\cdot5}\cdot\dfrac{5^2}{4\cdot6}\cdot\dfrac{5^2}{4\cdot6}\)
4. \(D=\left(\dfrac{4}{5}-\dfrac{1}{6}\right)\cdot\left(\dfrac{2}{3}\cdot\dfrac{1}{4}\right)^2\)
5. Cho \(M=8\dfrac{2}{7}-\left(3\dfrac{4}{9}+4\dfrac{2}{7}\right)\) ; \(N=\left(10\dfrac{2}{9}+2\dfrac{3}{5}\right)-6\dfrac{2}{9}\). Tính \(P=M-N\)
6. \(E=10101\left(\dfrac{5}{111111}+\dfrac{5}{222222}-\dfrac{4}{3\cdot7\cdot11\cdot13\cdot37}\right)\)
7. \(F=\dfrac{\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{1}{13}}{\dfrac{2}{3}+\dfrac{2}{7}-\dfrac{2}{13}}\cdot\dfrac{\dfrac{3}{4}-\dfrac{3}{16}-\dfrac{3}{256}+\dfrac{3}{64}}{1-\dfrac{1}{4}+\dfrac{1}{16}-\dfrac{1}{64}}+\dfrac{5}{8}\)
8. \(G=\text{[}\dfrac{\left(6-4\dfrac{1}{2}\right):0,03}{\left(3\dfrac{1}{20}-2,65\right)\cdot4+\dfrac{2}{5}}-\dfrac{\left(0,3-\dfrac{3}{20}\right)\cdot1\dfrac{1}{2}}{\left(1,88+2\dfrac{3}{25}\right)\cdot\dfrac{1}{80}}\text{]}:\dfrac{49}{60}\)
9. \(H=\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+\dfrac{1}{4\cdot5\cdot6}+...+\dfrac{1}{98\cdot99\cdot100}\)
10. \(I=\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot\dfrac{24}{25}\cdot...\cdot\dfrac{2499}{2500}\)
11. \(K=\left(-1\dfrac{1}{2}\right)\left(-1\dfrac{1}{3}\right)\left(-1\dfrac{1}{4}\right)...\left(-1\dfrac{1}{999}\right)\)
12. \(L=1\dfrac{1}{3}+1\dfrac{1}{8}+1\dfrac{1}{15}...\) (98 thừa số)
13. \(M=-2+\dfrac{1}{-2+\dfrac{1}{-2+\dfrac{1}{-2+\dfrac{1}{3}}}}\)
14. \(N=\dfrac{155-\dfrac{10}{7}-\dfrac{5}{11}+\dfrac{5}{23}}{403-\dfrac{26}{7}-\dfrac{13}{11}+\dfrac{13}{23}}\)
15. \(P=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{5}-1\right)...\left(\dfrac{1}{2001}-1\right)\)
16. \(Q=\left(\dfrac{1}{1\cdot2}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{2005\cdot2006}\right):\left(\dfrac{1}{1004\cdot2006}+\dfrac{1}{1005\cdot2005}+...+\dfrac{1}{2006\cdot1004}\right)\)
Thực hiện phép tính, tính nhanh nếu có thể
a, \(\dfrac{7}{13}\) + \(\dfrac{12}{13}\) + \(\dfrac{6}{-13}\)
b, ( \(\dfrac{4}{5}\) + \(\dfrac{1}{2}\) ) x ( \(\dfrac{6}{13}\) - 2 )
c, 75% : \(\dfrac{1}{2}\) - \(2\dfrac{1}{2}\) x ( \(-1\dfrac{1}{3}\) )
d, 0,375 x \(1\dfrac{3}{5}\) + 60% x \(\dfrac{2}{7}\) + \(\dfrac{3}{5}\) x \(\dfrac{5}{7}\)
e, \(\dfrac{-5}{6}\) x \(\dfrac{7}{13}\) + \(\dfrac{19}{13}\) : \(\dfrac{6}{-5}\) + \(\dfrac{2}{5}\)
f, 1,25 x \(\dfrac{7}{9}+\dfrac{5}{4}x\dfrac{15}{9}-1\dfrac{1}{4}:\dfrac{19}{3}\)
Tính nhanh:
P = \(\dfrac{\dfrac{2}{3}-\dfrac{1}{4}+\dfrac{5}{11}}{\dfrac{5}{12}+1-\dfrac{7}{11}}\)
Tính nhanh :
\(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}{\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\right)-\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}\)
so sánh 2004/2005+2005/2006 và 2004+2005/2005+2006
Tính A/B
A=
\(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2021}\)
B=
\(\dfrac{1}{2020}+\dfrac{2}{2019}+\dfrac{3}{2018}+...+\dfrac{2019}{2}+\dfrac{2020}{1}\)
Bài 1:Thực hiện phép tính (tính hợp lý nếu có thể)
1) \(\dfrac{8}{31}\) +\(\dfrac{-12}{25}\) +\(\dfrac{23}{31}\) +\(\dfrac{-13}{25}\)
2) \(\dfrac{1}{2}\) + \(\dfrac{3}{4}\) - ( \(\dfrac{3}{4}\) - \(\dfrac{4}{5}\) )
3) \(\dfrac{7}{3}\) . \(\dfrac{-5}{2}\) . \(\dfrac{15}{21}\) .\(\dfrac{4}{-5}\)
4)\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\) : ( \(-\dfrac{6}{7}\) )
5) (\(\dfrac{3}{29}\) - \(\dfrac{1}{5}\) ) . \(\dfrac{29}{3}\)
6) \(\dfrac{5}{7}\) . \(\dfrac{5}{11}\) + \(\dfrac{5}{7}\) . \(\dfrac{2}{11}\) - \(\dfrac{5}{7}\) .\(\dfrac{14}{11}\)
7)\(\dfrac{-11}{12}\) . \(\dfrac{1}{8}\) + \(\dfrac{11}{12}\) .\(\dfrac{-3}{16}\) -\(\dfrac{11}{12}\)
8) \(\dfrac{7}{4}\) . \(\dfrac{29}{5}\) -\(\dfrac{7}{9}\) .\(\dfrac{9}{4}\) +\(3\dfrac{2}{13}\)
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