\(C=\frac{1}{3}.\frac{1}{7}+\frac{1}{7}.\frac{1}{11}+\frac{1}{11}.\frac{1}{15}+...+\frac...">
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22 tháng 3 2016

rút gọn chứ ko fai tính à

23 tháng 12 2016

\(C=\frac{1}{3}.\frac{1}{7}+\frac{1}{7}.\frac{1}{11}+\frac{1}{11}.\frac{1}{13}+...+\frac{1}{2011}.\frac{1}{2015}\)

\(C=\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.13}+...+\frac{1}{2011.2015}\)

\(4C=4\left(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.13}+...+\frac{1}{2011.2015}\right)\)

\(4C=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.13}+...+\frac{4}{2011.2015}\)

\(4C=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+...+\frac{1}{2011}-\frac{1}{2015}\)

\(4C=\frac{1}{3}-\frac{1}{2015}=\frac{2012}{6045}\)

\(C=\frac{2012}{6045}:4=\frac{503}{6045}\)

24 tháng 7 2019

a) \(\frac{4}{11}-\frac{7}{15}+\frac{7}{11}-\frac{5}{15}\)

\(=\left(\frac{4}{11}+\frac{7}{11}\right)-\left(\frac{7}{15}+\frac{5}{15}\right)\)

\(=1-\frac{4}{5}\)

\(=\frac{1}{5}\)

b) \(\frac{7}{3}-\frac{4}{9}-\frac{1}{3}-\frac{5}{9}\)

\(=\left(\frac{7}{3}-\frac{1}{3}\right)-\left(\frac{4}{9}+\frac{5}{9}\right)\)

\(=2-1\)

\(=1\)

c) \(\frac{1}{4}+\frac{7}{33}-\frac{5}{3}\)

\(=\frac{-1}{4}+\frac{-16}{11}\)

\(=\frac{-75}{44}\)

d) \(\frac{-3}{4}\times\frac{8}{11}-\frac{3}{11}\times\frac{1}{2}\)

\(=\frac{-6}{11}-\frac{3}{22}\)

\(=\frac{15}{22}\)

e) \(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\) 

\(=\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}+\frac{1}{11\times13}+\frac{1}{13\times15}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)

\(=\frac{1}{3}-\frac{1}{15}\)

\(=\frac{4}{15}\)

10 tháng 6 2015

\(P=\frac{\frac{2}{3}-\frac{1}{4}+\frac{5}{11}}{\frac{5}{12}+1-\frac{7}{11}}=\frac{\frac{115}{132}}{\frac{103}{132}}=\frac{115}{132}\cdot\frac{132}{103}=\frac{115}{103}\)

30 tháng 5 2016

a. \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}=\frac{15}{13.2}-\frac{2}{13}=\frac{15}{13.2}-\frac{2.2}{13.2}=\frac{15-4}{26}=\frac{11}{26}\)

 

30 tháng 5 2016

C. \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}=\frac{1}{23}.\left(-11.\frac{6}{7}-11.\frac{8}{7}-1\right)=\frac{1}{23}.\left(-22-1\right)=\frac{1}{23}.\left(-23\right)=-1\)

2: \(=\dfrac{0.8}{\dfrac{16}{25}-\dfrac{1}{25}}+\dfrac{\dfrac{71}{75}\cdot\dfrac{7}{4}}{\dfrac{119}{36}\cdot\dfrac{36}{17}}\)

\(=\dfrac{4}{5}\cdot\dfrac{5}{3}+\dfrac{71}{300}=\dfrac{471}{300}=\dfrac{157}{100}\)

3: \(=\dfrac{\dfrac{2}{5}-\dfrac{2}{9}+\dfrac{2}{11}}{\dfrac{7}{5}-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{2}{6}-\dfrac{2}{8}+\dfrac{2}{10}}{\dfrac{7}{6}-\dfrac{7}{8}+\dfrac{7}{10}}\)

=2/7-2/7=0

31 tháng 1 2020

\(A=\frac{2015+2013+2011+...+5+3+1}{2015-2013+2011-2009+...+7-5+3-1}\)

Ta có : 2015 + 2013 + 2011 + ... + 5 + 3 + 1  

= [(2015 - 1) : 2 + 1].(2015 + 1) : 2

= 1008.2016 : 2 = 1016064

Lại có :  2015 - 2013 + 2011 - 2009 + ... + 7 - 5 + 3 - 1 (1008 số hạng

= (2015 - 2013) + (2011 - 2009) + ... + (7 - 5) + (3 - 1) (504 cặp)

= 2 + 2 + ... + 2 + 2 (504 số hạng 2)

= 2 x 504 = 1008 

Khi đó A = \(\frac{1016064}{1008}=1008\)

b) tTa có : B = \(\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+...+\frac{1}{97.3}+\frac{1}{99.1}}\)

=> \(\frac{B}{100}\) = \(\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{\frac{100}{1.99}+\frac{100}{3.97}+\frac{100}{5.95}+...+\frac{100}{97.3}+\frac{100}{99.1}}\)

\(=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{1+\frac{1}{99}+\frac{1}{3}+\frac{1}{97}+\frac{1}{5}+\frac{1}{95}+..+\frac{1}{97}+\frac{1}{3}+\frac{1}{99}+1}=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{2\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}\right)}=\frac{1}{2}\)

Khi đó : B/100 = 1/2

=> B = 50 

Vậy B = 50

6 tháng 2 2020

giỏi ghê vậy Hân

9 tháng 4 2018

a) 2/7+-3/8+11/7+1/3+1/7+5/-8

=(2/7+11/7+1/7)+(3/8+-5/8)+1/3

=2+2+1/3

=4+1/3

=13/3

b) -3/8+12/25+5/-8+2/-5+13/25

=(-3/8+-5/8)+(12/25+13/25)+-2/5

=-1+1+-2/5

=0+-2/5

=-2/5

c)7/8+1/8*3/8+1/8*5/8

=7/8+1/8*(3/8+5/8)

=7/8+1/8*1

=7/8+1/8

=1

9 tháng 4 2018

a) 2/7+-3/8+11/7+1/3+1/7+5/-8

=(2/7+11/7+1/7)+(3/8+-5/8)+1/3

=2+2+1/3

=4+1/3

=13/3

b) -3/8+12/25+5/-8+2/-5+13/25

=(-3/8+-5/8)+(12/25+13/25)+-2/5

=-1+1+-2/5

=0+-2/5

=-2/5

c)7/8+1/8*3/8+1/8*5/8

=7/8+1/8*(3/8+5/8)

=7/8+1/8*1

=7/8+1/8

=1