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. \(Q=\left(\dfrac{1}{1\cdot2}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{2005\cdot2006}\right):\left(\dfrac{1}{1004\cdot2006}+\dfrac{1}{1005\cdot2005}+...+\dfrac{1}{2006\cdot1004}\right)\)
Tính giá trị của biểu thức sau:
\(D=\left(1+\dfrac{1}{1\cdot3}\right)\cdot\left(1+\dfrac{1}{2\cdot4}\right)\cdot\left(1+\dfrac{1}{3\cdot5}\right)\cdot...\cdot\left(1+\dfrac{1}{2019\cdot2021}\right)\)
\(a.19\dfrac{5}{8}:\dfrac{7}{12}-15\dfrac{1}{4}:\dfrac{7}{12} b.\dfrac{2}{5}.\dfrac{1}{3}-\dfrac{2}{15}:\dfrac{1}{5}+\dfrac{3}{5}.\dfrac{1}{3}\)
c.\(\left(3\dfrac{1}{3}+2,5\right):\left(3\dfrac{1}{6}-\left(4\dfrac{1}{5}\right)\right)-\dfrac{11}{31}\)
1.Tính giái trị biểu thức
\(a,\left(\dfrac{4}{9}+\dfrac{1}{3}\right)^2\)
\(b,\left(\dfrac{1}{2}-\dfrac{3}{5}\right)^3\)
c,\(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{-6}{4}\right)^4\)
\(\left(\dfrac{3}{4}\right)^3:\left(\dfrac{3}{4}\right)^2:\left(\dfrac{-3}{2}\right)^3\)
A) TÌM X, BIẾT:
\(\left(\dfrac{1}{1.101}+\dfrac{1}{2.102}+...+\dfrac{1}{10.110}\right).x=\dfrac{1}{1.11}+\dfrac{1}{2.12}+...+\dfrac{1}{100.110}\)
B) CHỨNG TỎ RẰNG:
a/ \(S=\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}< \dfrac{1}{2}\)
b/ \(S=\dfrac{1}{41}+\dfrac{1}{42}+...+\dfrac{1}{80}>\dfrac{7}{12}\)
c/ \(S=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}< 1\)
d/ \(\dfrac{49}{100}< S=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{99^2}< 1\)
C)
a/ Tìm giá trị lớn nhất của các biểu thức sau, đồng thời tìm x để các biểu thức này đạt giá trị lớn nhất:
\(A=2018-\left|10-x\right|\)
\(B=1999-\left(x+2\right)^2\)
b) Tìm giá trị nhỏ nhất của các biểu thức sau, đồng thời tìm x để các biểu thức này đạt giá trị nhỏ nhất:
\(A=\left(2x-8\right)^2+3\)
\(B=\left|x^2-25\right|-2017\)
Bài 1 : Tìm các số nguyên x , biết :
a) \(\dfrac{2}{3}\left(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{1}{3}\right)\le\dfrac{x}{18}\le\dfrac{7}{13}\left(\dfrac{1}{2}-\dfrac{1}{6}\right)\)
b) \(\left(\dfrac{31}{20}-\dfrac{26}{45}\right).-\dfrac{36}{35}< x< \left(\dfrac{51}{56}+\dfrac{8}{21}+\dfrac{1}{3}\right).\dfrac{8}{13}\)
Bài 2 :
C = \(\dfrac{-1}{3}.\dfrac{141}{17}-\dfrac{39}{9}.\dfrac{-1}{7}\)
\(E=\left[\dfrac{1919}{2121}-\dfrac{54}{99}+\left(\dfrac{2456}{3799}\right)^5\right]\cdot\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\)
A=\(\left(\dfrac{1}{2}-1\right).\left(\dfrac{1}{3}-1\right).\left(\dfrac{1}{4}-4\right).......\left(\dfrac{1}{99}-1\right).\left(\dfrac{1}{100}-1\right)\)
1:Tính
a) \(\left(\dfrac{1}{7}.x-\dfrac{2}{7}\right).\left(\dfrac{-1}{5}.x-\dfrac{2}{5}\right)=0\)
b) \(\dfrac{1}{6}.x+\dfrac{1}{10}.x-\dfrac{4}{5}.x+1=0\)
2:So sánh:
a) A=\(\left(\dfrac{-46}{51}.0,32.\dfrac{17}{20}\right):\dfrac{64}{75}\)
B=\(\dfrac{-10}{11}.\dfrac{8}{9}+\dfrac{7}{8}.\dfrac{10}{11}\)
b) A=\(\dfrac{-1}{3}+\dfrac{0,2-0,375+\dfrac{5}{11}}{-0,3+\dfrac{9}{16}-\dfrac{15}{22}}\)
B=\(\dfrac{-43}{51}.\dfrac{19}{80}\)
