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30 tháng 6 2017

\(X-\left(\frac{31}{5}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\frac{9}{13}\)

\(X-\left(\frac{31}{5}+\frac{31}{3\cdot5}+\frac{31}{5\cdot7}+\frac{31}{7\cdot9}+\frac{31}{9\cdot11}+\frac{31}{11\cdot13}\right)=\frac{9}{13}\)

\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)

\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)

\(X-\left[\frac{31}{2}\cdot\frac{10}{39}+\frac{31}{5}\right]=\frac{9}{13}\)

\(X-\frac{1984}{195}=\frac{9}{13}\)

\(\Rightarrow X=\frac{9}{13}+\frac{1984}{195}=\frac{163}{15}\)

29 tháng 6 2017

163 / 15

mk nghĩ v

25 tháng 6 2018

\(\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}=\frac{31}{1.3}+\frac{31}{3.5}+\frac{31}{5.7}+\frac{31}{7.9}+\frac{31}{9.11}+\frac{31}{11.13}\\ \)

\(=\frac{31}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)

\(=\frac{31}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=\frac{31}{2}.\left(1-\frac{1}{13}\right)=\frac{31}{2}.\frac{12}{13}=\frac{31.6}{13}=\frac{186}{13}\)

\(\Rightarrow x-\frac{186}{13}=\frac{9}{13}\Leftrightarrow x=\frac{195}{13}=15\)

25 tháng 6 2018

\(x-\left(\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\)\(\frac{9}{13}\)(1)

Đặt \(A=\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\)

\(A=31\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\right)\)

\(\Rightarrow2A=31\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)

\(2A=31\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)

\(2A=31\left(2-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(2A=31\left(2-\frac{1}{13}\right)\)

\(2A=31.\frac{25}{13}\)

\(2A=\frac{775}{13}\)

\(\Rightarrow A=\frac{775}{13}:2\)

\(A=\frac{775}{26}\)

   Thay vào (1) ta có:

 \(x-\frac{775}{26}=\frac{9}{13}\)

\(\Leftrightarrow x=\frac{9}{13}+\frac{775}{26}\)

\(\Leftrightarrow x=\frac{61}{2}\)

23 tháng 6 2016

\(A=17\frac{2}{31}-\left(\frac{15}{17}+6\frac{2}{31}\right)=\left(17\frac{2}{31}-6\frac{2}{31}\right)-\frac{15}{17}=11-\frac{15}{17}=10+\left(1-\frac{15}{17}\right)=10\frac{2}{17}\)

23 tháng 6 2016

\(B=\left(31\frac{6}{13}-36\frac{6}{13}\right)+5\frac{9}{41}=-5+5\frac{9}{41}=\frac{9}{41}\)

C=\(\left(27\frac{51}{59}-7\frac{51}{59}\right)+\frac{1}{3}=20+\frac{1}{3}=20\frac{1}{3}\)

\(D=\left(13\frac{29}{31}-2\frac{28}{31}\right)+\left(4-3\frac{7}{8}\right)=11\frac{1}{31}+\frac{1}{8}=11\frac{8+31}{31.8}=11\frac{39}{248}\)

31 tháng 3 2019

a, \(\left(31\frac{6}{13}+5\frac{9}{41}\right)-36\frac{6}{13}=31\frac{6}{16}+5\frac{9}{41}-36\frac{6}{13}\)

\(=\left(31\frac{6}{16}-31\frac{6}{16}\right)+5\frac{9}{41}\)

\(=0+5\frac{9}{41}=5\frac{9}{41}\)

b, \(\left(17\frac{29}{31}-3\frac{7}{8}\right)-\left(2\frac{28}{31}-4\right)=17\frac{9}{31}-3\frac{7}{8}-2\frac{28}{31}+4\)

28 tháng 7 2016

Ta có : 

Đặt \(A=\frac{31}{3}+\frac{31}{15}+...+\frac{31}{143}\)

\(A=\frac{31}{1.3}+\frac{31}{3.5}+...+\frac{31}{11.13}\)

\(\frac{2}{31}A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)

\(\frac{2}{31}A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)

\(\frac{2}{31}A=1-\frac{1}{13}\)

\(A=\frac{12}{13}:\frac{2}{31}\)

\(A=\frac{186}{13}\)

\(\Rightarrow x-\frac{186}{13}=\frac{9}{13}\)

\(x=\frac{9}{13}+\frac{186}{13}\)

\(x=\frac{195}{13}=15\)

Ủng hộ mk nha !!! ^_^

\(\text{Đặt }A=\frac{31}{3}+\frac{31}{15}+...+\frac{31}{143}\)

\(\Rightarrow A=\frac{31}{1.3}+\frac{31}{3.5}+...+\frac{31}{11.13}\)

\(\Rightarrow\frac{2}{31}A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)

\(\Rightarrow\frac{2}{31}A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)

\(\Rightarrow\frac{2}{31}A=1-\frac{1}{13}\Rightarrow A=\frac{12}{13}:\frac{2}{31}=\frac{186}{13}\)

\(\Rightarrow x-\frac{186}{13}=\frac{9}{13}\)

\(\Rightarrow x=\frac{9}{13}+\frac{186}{13}\)

\(\Rightarrow x=\frac{195}{13}=15\)

12 tháng 2 2016

hay doi hon so thanh phan  so de tinh cho de nhe

 

12 tháng 2 2016

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