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29 tháng 9 2017

Ta đặt  \(A=1+5+5^2+......+5^9\Rightarrow5A=5+5^2+...+5^9+5^{10}\)

\(\Rightarrow4A=5^{10}-1\Rightarrow A=\frac{5^{10}-1}{4}\)

tTương tự \(B=1+5+5^2+......+5^8\Rightarrow B=\frac{5^9-1}{4}\)

\(C=1+3+3^2+......+3^9\Rightarrow C=\frac{3^{10}-1}{3}\)

\(D=1+3+3^2+......+3^8\Rightarrow D=\frac{3^9-1}{3}\)

Vậy \(\frac{A}{B}=\frac{5^{10}-1}{5^9-1}=\frac{5\left(5^9-1\right)+4}{5^9-1}=5+\frac{4}{5^9-1}\)

\(\frac{C}{D}=\frac{3^{10}-1}{3^9-1}=\frac{3\left(3^9-1\right)+3}{3^9-1}=3+\frac{3}{3^9-1}\)

Ta thấy \(\frac{3}{3^9-1}< 1\Rightarrow3+\frac{3}{3^9-1}< 4< 5< 5+\frac{5}{5^9-1}\)

Vậy \(\frac{A}{B}>\frac{C}{D}\)  hay \(\frac{1+5+5^2+...+5^9}{1+5+5^2+...+5^8}>\frac{1+3+3^2+...+3^9}{1+3+3^2+...+3^8}\)

17 tháng 12 2016

a) \(\frac{17}{9}-\frac{17}{9}:\left(\frac{7}{3}+\frac{1}{2}\right)\)

= \(\frac{17}{9}-\frac{17}{9}:\frac{17}{6}\)

= \(\frac{17}{9}-\frac{2}{3}\)

= \(\frac{11}{9}\)

b) \(\frac{4}{3}.\frac{2}{5}-\frac{3}{4}.\frac{2}{5}\)

= \(\frac{2}{5}.\left(\frac{4}{3}-\frac{3}{4}\right)\)

= \(\frac{2}{5}.\frac{7}{12}\)

= \(\frac{7}{30}\)

Mình lười làm quá, hay mình nói kết quả cho bn thôi nha

c) -6

d) 3

e) 3

g) 12

h) \(\frac{23}{18}\)

i) \(\frac{-69}{20}\)

k) \(\frac{-1}{2}\)

l) \(\frac{49}{5}\)

24 tháng 6 2018

\(\frac{A}{B}=\frac{\frac{9}{1}+\frac{8}{2}+\frac{7}{3}+\frac{6}{4}+\frac{5}{5}+\frac{4}{6}+\frac{3}{7}+\frac{2}{8}+\frac{2}{9}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}}\)

\(\frac{A}{B}=\frac{\left(\frac{8}{2}+1\right)+\left(\frac{7}{3}+1\right)+...+\left(\frac{1}{9}+1\right)+1}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}}\)

\(\frac{A}{B}=\frac{\frac{10}{2}+\frac{10}{3}+\frac{10}{4}+...+\frac{10}{9}+\frac{10}{10}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}}\)

\(\frac{A}{B}=\frac{10\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}}\)

\(\frac{A}{B}=10\)

24 tháng 6 2018

\(A=\frac{9}{1}+\frac{8}{2}+\frac{7}{3}+...+\frac{2}{8}+\frac{1}{9}\)

Tách 9=1+1+...+1 ( có 9 số 1)

\(\Rightarrow A=1+\left(\frac{8}{2}+1\right)+\left(\frac{7}{3}+1\right)+...+\left(\frac{2}{8}+1\right)+\left(\frac{1}{9}+1\right)\)

\(A=\frac{10}{10}+\frac{10}{2}+\frac{10}{3}+...+\frac{10}{8}+\frac{10}{9}\)

\(A=10.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)\)

\(\Rightarrow A:B=\frac{10.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}}=10\) ( vì \(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\ne0\) )

Vậy \(A:B=10\)

25 tháng 7 2017

\(=\frac{16}{5}.\frac{15}{16}-\left(\frac{3}{4}+\frac{2}{7}\right):\left(\frac{-29}{28}\right)\)

\(=3-\left(\frac{21}{28}+\frac{8}{28}\right):\left(\frac{-29}{28}\right)\)

\(=3-\left(\frac{29}{28}\right).\left(\frac{-28}{29}\right)\)

\(=3-\left(-1\right)\)

\(=4\)

b)   \(=\left(\frac{1}{4}+\frac{25}{2}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3}{8}-\frac{1}{12}\right)\right)\)

       \(=\left(\frac{4}{16}+\frac{200}{16}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3.3}{2.3.4}-\frac{2}{2.3.4}\right)\right)\)

     \(=\left(\frac{199}{16}\right):\left(12-\frac{7}{12}:\left(\frac{9}{24}-\frac{2}{24}\right)\right)\)

      \(=\frac{199}{16}:\left(12-\frac{7}{12}.\frac{24}{7}\right)\)

    \(=\frac{199}{16}:\left(12-2\right)\)

\(=\frac{199}{16}:10\)

\(=\frac{199}{160}\)

c)   \(\left(\frac{-3}{5}+\frac{5}{11}\right):\frac{-3}{7}+\left(\frac{-2}{5}+\frac{6}{5}\right):\frac{-3}{7}\)

\(\left(\frac{-33}{55}+\frac{25}{55}\right):\frac{-3}{7}+\left(\frac{4}{5}\right):\frac{-3}{7}\)

\(\left(\frac{-8}{55}\right).\frac{-7}{3}+\frac{4}{5}.\frac{-7}{3}\)

\(\frac{-7}{3}\left(\frac{-8}{55}+\frac{4}{5}\right)\)

\(\frac{-7}{3}.\frac{36}{55}=\frac{-84}{55}\)

     

25 tháng 7 2017

giờ mk phải đi ngủ r mai mk làm cho 

27 tháng 6 2019

Những câu từ D trở đi là các câu riêng biệt ak bạn

2 tháng 7 2019

\(A = {1\over2}-{3\over4}+{5\over6}-{7\over12}={6\over12}-{9\over12}+{10\over12}-{7\over12}\)\(={0\over12}=0\)

12 tháng 12 2019

a) \(\left(-\frac{5}{2}\right)^2:\left(-15\right)-\left(-0,45+\frac{3}{4}\right).\left(-1\frac{5}{9}\right)\)

\(-\frac{25}{4}:\left(-15\right)-\left(\frac{9}{20}+\frac{15}{20}\right).\left(-\frac{14}{9}\right)\)

=\(-\frac{25}{4}.\frac{1}{-15}-\frac{6}{5}.\left(-\frac{14}{9}\right)\)

\(\frac{-5}{12}-\frac{8}{5}\)

\(\frac{\left(-25\right)-96}{60}\)

\(\frac{\left(-25\right)+\left(-96\right)}{60}\)

=\(\frac{121}{60}\)

b) \(\left(\frac{-1}{3}\right)-\left(\frac{-3}{5}\right)^0+\left(1-\frac{1}{2}\right)^2:2\)

\(\left(\frac{-1}{3}\right)-1+\left(\frac{1}{2}\right)^2.\frac{1}{2}\)

=\(\left(\frac{-1}{3}\right)-\frac{3}{3}+\frac{1}{4}.\frac{1}{2}\)

\(\frac{-4}{3}+\frac{1}{8}\)=\(\frac{-32+3}{24}\)

=\(\frac{-29}{24}\)

c) E=\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)

     =\(\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.6^9}{2^{10}.3^8+6^8.20}\)

     =\(\frac{2^{10}.3^8-2.6^9}{2^{10}.3^8+6^8.20}\)

     =\(\frac{3}{5}\)

d)\(\frac{5^4.20^4}{25^5.4^5}\)

=\(\frac{\left(5.20\right)^4}{\left(25.4\right)^5}\)

=\(\frac{100^4}{100^5}\)

=\(\frac{1}{100}\)