Các câu hỏi tương tự
Chứng minh
\(\frac{1}{5}+\frac{1}{13}+\frac{1}{25}+....+\frac{1}{10^2+11^2}<\frac{9}{20}\)
a)\(\frac{-5}{7}.\left(\frac{2}{11}+\frac{9}{5}\right)+\left(\frac{-9}{11}+\frac{4}{5}\right).\frac{5}{7}\) b)\(2\frac{2}{5}.\frac{5}{9}+1\frac{4}{9}.\frac{12}{5}-1,8.\frac{10}{3}\)c)\(\frac{-7}{25}.\frac{11}{13}+\frac{-7}{25}.\frac{4}{13}-\frac{2}{13}.\frac{-7}{25}\)
Mk cần giải bài này:
Bài 1: Chứng minh rằng
a) B= 3/10 + 3/11 + 3/12 + 3/13 + 3/14 ko phải là số tự nhiên.
b) C=\(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{9^2}.\) Chứng tỏ \(\frac{2}{5}< C< \frac{8}{9}\)
chứng tỏ rằng :\(\frac{1}{8}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{41}+\frac{1}{42}+\frac{1}{43}< \frac{1}{2}\)
Chứng minh rằng :
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)
Tính giá trị biểu thức :1. Afrac{frac{2}{5}+frac{2}{7}-frac{2}{9}-frac{2}{11}}{frac{4}{5}+frac{4}{7}-frac{4}{9}-frac{4}{11}} 2. Bfrac{1^2}{1.2}.frac{2^2}{2.3}.frac{3^2}{3.4}.frac{4^2}{4.5}3. Cfrac{2^2}{1.3}.frac{3^2}{2.4}.frac{4^2}{3.5}.frac{5^2}{4.6}4. D(frac {150}{1111}+frac{5}{75}-frac{14}{77})(frac{1}{5}-frac{1}{6}-frac{1}{30}) 5. Cho M8frac{2}{7}-left(3frac{4}{9}+3frac{9}{7}right);Nleft(10frac{2}{9}+2frac{3}{5}right)-6frac{2}{9}. Tính PM-N6. E10101left(frac{5}{111111}+frac{5}{222222}-frac{4...
Đọc tiếp
Tính giá trị biểu thức :
1. \(A=\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
2. \(B=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.\frac{4^2}{4.5}\)
3. \(C=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4.6}\)
4. \(D=(\frac {150}{1111}+\frac{5}{75}-\frac{14}{77})(\frac{1}{5}-\frac{1}{6}-\frac{1}{30}) \)
5. Cho \(M=8\frac{2}{7}-\left(3\frac{4}{9}+3\frac{9}{7}\right);N=\left(10\frac{2}{9}+2\frac{3}{5}\right)-6\frac{2}{9}\). Tính \(P=M-N\)
6. \(E=10101\left(\frac{5}{111111}+\frac{5}{222222}-\frac{4}{3.7.11.13.37}\right)\)
7. \(F=\frac{\frac{1}{3}+\frac{1}{7}-\frac{1}{13}}{\frac{2}{3}+\frac{2}{7}-\frac{2}{13}}.\frac{\frac{3}{4}-\frac{3}{16}-\frac{3}{256}+\frac{3}{64}}{1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}}+\frac{5}{8}\)
8. \(G=\left[\frac{\left(6-4\frac{1}{2}\right):0,03}{\left(3\frac{1}{20}-2,65\right).4+\frac{2}{5}}-\frac{\left(0,3-\frac{3}{20}\right).1\frac{1}{2}}{\left(1,88+2\frac{3}{25}\right).\frac{1}{80}}\right]:\frac{49}{60}\)
9. \(H=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{4.5.6}+...+\frac{1}{98.99.100}\)
10. \(I=\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.....\frac{2499}{2500}\)
11. \(k=\left(-1\frac{1}{2}\right)\left(-1\frac{1}{3}\right)\left(-1\frac{1}{4}\right)...\left(-1\frac{1}{999}\right)\)
12. \(L=1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}...\)(98 thừa số)
13. \(M=-2+\frac{1}{-2+\frac{1}{-2+\frac{1}{-2+\frac{1}{3}}}}\)
14. \(N=\frac{155-\frac{10}{7}-\frac{5}{11}+\frac{5}{23}}{403-\frac{26}{7}-\frac{13}{11}+\frac{13}{23}}\)
15. \(P=\left(\frac{1}{4}-1\right)\left(\frac{1}{5}-1\right)...\left(\frac{1}{2000}-1\right)\left(\frac{1}{2001}-1\right)\)
16. \(Q=\left(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{2005.2006}\right):\left(\frac{1}{1004.2006}+\frac{1}{1005.2005}+...+\frac{1}{2006.1004}\right)\)
Bài 1 : Cho A = \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}...\frac{79}{80}\)
Chứng minh rằng A < \(\frac{1}{9}\)
Bài 4 : Chứng minh rằng: 1.3.5.7....19 = \(\frac{11}{2}.\frac{12}{2}.\frac{13}{2}...\frac{20}{2}\)
Câu 1: Chứng tỏ rằng:
\(\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+...+\frac{1}{26}+\frac{1}{27}>\frac{8}{27}\)
Câu 2: Tính:
\(D=\frac{2^{10}.6^{15}+3^{14}.15.4^{13}}{2^{18}.18^7.3^3+3^{15}.2^{25}}\)
Chứng tỏ rằng:
A=\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\)
Thì 1<A<2