Tìm x thuộc N
\(x-\frac{20}{11\cdot13}-\frac{20}{13\cdot15}-\frac{20}{15\cdot17}-...-\frac{20}{53\cdot55}=\frac{3}{11}\)
\(x+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}=\frac{2}{7}\)
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1 tháng 7 2018
Sửa đề : \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Leftrightarrow\)\(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Leftrightarrow\)\(2\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)
\(\Leftrightarrow\)\(2\left(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)
\(\Leftrightarrow\)\(2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\Leftrightarrow\)\(2\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\Leftrightarrow\)\(\frac{1}{6}-\frac{1}{x+1}=\frac{2}{9}.\frac{1}{2}\)
\(\Leftrightarrow\)\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
\(\Leftrightarrow\)\(\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}\)
\(\Leftrightarrow\)\(\frac{1}{x+1}=\frac{1}{18}\)
\(\Leftrightarrow\)\(x+1=18\)
\(\Leftrightarrow\)\(x=18-1\)
\(\Leftrightarrow\)\(x=17\)
Vậy \(x=17\)
Chúc bạn học tốt ~
1 tháng 7 2018
\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+10.\frac{4}{55}=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+\frac{40}{55}=\frac{3}{11}\)
\(\Leftrightarrow\)\(x=\frac{3}{11}-\frac{40}{55}\)
\(\Leftrightarrow\)\(x=\frac{-5}{11}\)
Vậy \(x=\frac{-5}{11}\)
Chúc bạn học tốt ~
DP
13 tháng 7 2017
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+....+\frac{1}{97.100}=\frac{0,33.x}{2009}\)
\(\Leftrightarrow\frac{1}{3}\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{97}-\frac{1}{100}\right)=\frac{0,33.x}{2009}\)
\(\Leftrightarrow\frac{1}{3}\cdot\left(1-\frac{1}{100}\right)=\frac{0,33.x}{2009}\)
\(\Leftrightarrow\frac{1}{3}\cdot\frac{99}{100}=\frac{0,33.x}{2009}\)
\(\Leftrightarrow\frac{33}{100}=\frac{0,33.x}{2009}\)
\(\Leftrightarrow x=\frac{0,33\times100}{0,33}=100\)
2 tháng 3 2016
(2/143+2/195+2/255+2/323+2/399).462-y=19
=> 10/231.462-y=19
=> 20-y=19
=> y= 20-19=1
DUYỆT NHA "T I C K"
DP
24 tháng 6 2017
\(a,\)\(x+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}=-\frac{37}{45}\)
\(x+\left(\frac{9-5}{5.9}+\frac{13-9}{9.13}+\frac{17-13}{13.17}+...+\frac{45-41}{41.45}\right)=-\frac{37}{45}\)
\(x+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+....+\frac{1}{41}-\frac{1}{45}\right)-\frac{37}{45}\)
\(x+\left(\frac{1}{5}-\frac{1}{45}\right)=-\frac{37}{45}\)
\(x+\frac{8}{45}=-\frac{37}{45}\)
\(x=-\frac{37}{45}-\frac{8}{45}\)
\(x=-1\)
31 tháng 7 2016
\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10.\frac{4}{55}=\frac{3}{11}\)
\(x-\frac{40}{55}=\frac{3}{11}\)
\(x=\frac{3}{11}+\frac{40}{55}\)
\(x=\frac{55}{55}=1\)
nha.
23 tháng 2 2018
=> 1/11 - 1/13 + 1/13 - 1/15 + ..... + 1/19 - 1/21 - x + 4 + 221/231 = 7/3
=> 1/11 - 1/21 - x + 4 + 221/231 = 7/3
=> 2099/420 - x = 7/3
=> x = 2099/420 - 7/3 = 373/140
Tk mk nha
20 tháng 5 2020
Bài làm
\(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow2\left(\frac{1}{11.13}+\frac{1}{13.15}+...+\frac{1}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow2\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow2\left(\frac{1}{11}-\frac{1}{21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow2.\frac{10}{231}-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow\frac{20}{231}-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow\frac{20}{231}-x+\frac{924}{231}+\frac{221}{231}=\frac{539}{231}\)
\(\Leftrightarrow\frac{20}{231}-x+\frac{924}{231}=\frac{539}{231}-\frac{221}{231}\)
\(\Leftrightarrow\frac{20}{231}-x+\frac{924}{231}=\frac{318}{231}\)
\(\Leftrightarrow\frac{20}{231}-x=\frac{318}{231}-\frac{924}{231}\)
\(\Leftrightarrow\frac{20}{231}-x=-\frac{606}{231}\)
\(\Leftrightarrow x=\frac{20}{231}-\frac{606}{231}\)
\(\Leftrightarrow x=-\frac{586}{231}\)
Vậy \(\Leftrightarrow=-\frac{586}{231}\)