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26 tháng 7 2018

\(\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+....+\frac{1}{2014.2016}\)

\(=\frac{1}{2}\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+....+\frac{2}{2014.2016}\right)\)

\(=\frac{1}{2}\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+....+\frac{1}{2014}-\frac{1}{2016}\right)\)

\(=\frac{1}{2}\left(\frac{1}{4}-\frac{1}{2016}\right)\)

\(=\frac{503}{4032}\)

26 tháng 7 2018

Đáp án : \(\frac{503}{4032}\)

26 tháng 3 2018

tìm y đúng hơn là tính :

\(\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+\frac{1}{11\cdot14}+...+\frac{1}{y\left(y+3\right)}=\frac{98}{1545}\)

\(\Rightarrow\frac{1}{3}\left(\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+...+\frac{3}{y\left(y+3\right)}\right)=\frac{98}{1545}\)

\(\Rightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{y}-\frac{1}{y+3}\right)=\frac{98}{1545}\)

\(\Rightarrow\frac{1}{3}\left(\frac{1}{5}-\frac{1}{y+3}\right)=\frac{98}{1545}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{y+3}=\frac{98}{1545}\div\frac{1}{3}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{y+3}=\frac{98}{515}\)

\(\Rightarrow\frac{1}{y+3}=\frac{1}{5}-\frac{98}{515}\)

\(\Rightarrow\frac{1}{y+3}=\frac{5}{515}=\frac{1}{103}\)

\(\Rightarrow y+3=103\)

\(\Rightarrow y=100\)

26 tháng 3 2018

tính cái gì? hay là tìm y?

19 tháng 4 2017

a)1.2.3.4...9-1.2.3.4...8-1.2.3.4...8.8

=1.2.3.4...8(9-1-8)

=1.2.3.4...8.0

=0

b)(3.4.216)2/11.123.411-169=(3.22.216)2/11.213.222-236=32.24.232/11.235-236=32.226/235.(11-2)

=32.236/235.9=32.236/235.32=2

c)70.(131313/565656+131313/727272+131313/909090

=70.(13/56+13/72+13/90)

=70.39/70=39

d)1/4.9+1/9.14+1/14.19+...+1/64.69

=4/4.9.4+4/9.4.14+4/14.19.4+...+4/64.69.4.

=1/4.(4/4.9+4/9.14+4/14.19+...+4/64.69)

=1/4.(1/4-1/9+1/9-1/14+1/14-1/19+...+1/64-1/69)

=1/4.(1/4-1/69)

=1/4.65/276=65/1104

~~~~~~~~Chúc bạn học giỏi nhé !~~~~~~~~

19 tháng 4 2017

nhìu thế này sao mà làm nổi

10 tháng 4 2015

\(\frac{19}{20}-\frac{5}{6.7}-\frac{5}{7.8}-\frac{5}{8.9}-...-\frac{5}{59.60}\)

\(\frac{19}{20}-\left(\frac{5}{6.7}+\frac{5}{7.8}+\frac{5}{8.9}+...+\frac{5}{59.60}\right)\)

\(\frac{19}{20}-5\left(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{59.60}\right)\)

\(\frac{19}{20}-5\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{60}\right)\)

\(\frac{19}{20}-5\left(\frac{1}{6}-\frac{1}{60}\right)\)

\(\frac{19}{20}-5.\frac{3}{20}\)

\(\frac{19}{20}-\frac{3}{4}\) = \(\frac{1}{5}\)

28 tháng 9 2017

\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)

\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{2^{12}.\left(3^2\right)^{12}.\left(5^4\right)^3.3^3.\left(2^3\right)^3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.3^3.2^9}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{27}.5^{12}}\)

\(=\frac{3}{5^2}\)

\(=\frac{3}{25}\)

28 tháng 9 2017

Ta có: \(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)\(=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{27}.5^{12}}=\frac{3}{5^2}=\frac{3}{25}\)

9 tháng 8 2016

\(M=\frac{1.2.3.4.5...98.99}{10}\)

\(M=1.2.3.4.5.6.7.8.9.11.12...98.99\)

4 tháng 7 2016

\(\frac{5}{4.6}+\frac{5}{6.8}+\frac{5}{8.10}+....+\frac{5}{298.300}\)

\(=\frac{5}{2}.\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+....+\frac{2}{298.300}\right)\)

\(=\frac{5}{2}.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+....+\frac{1}{298}-\frac{1}{300}\right)\)

\(=\frac{5}{2}.\left(\frac{1}{4}-\frac{1}{300}\right)=\frac{5}{2}.\frac{37}{150}=\frac{37}{60}\)

Vậy..........