(X-\(\frac{1}{5}\)) :(\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\))=\(\frac{1}{5}\)
K
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14 tháng 9 2016
\(\Leftrightarrow\)\(\frac{1}{3}\)-\(\frac{1}{3}\)+\(\frac{1}{4}\)-\(\frac{1}{4}\)+\(\frac{1}{5}\)-....+\(\frac{1}{10}\)=x-\(\frac{113}{260}\)
\(\Leftrightarrow\)x-\(\frac{113}{260}\)=\(\frac{1}{10}\)
\(\Leftrightarrow\)x=\(\frac{139}{260}\)
7 tháng 8 2016
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
HJ
7 tháng 8 2017
\(a,\left(10\frac{2}{9}.2\frac{3}{5}\right)-6\frac{2}{9}=\frac{1196}{45}-\frac{56}{9}=\frac{1196}{45}-\frac{280}{45}=\frac{916}{45}\)
\(b,\frac{6}{7}+\frac{1}{7}.\frac{2}{7}+\frac{1}{7}.\frac{5}{7}=\frac{1}{7}\left(6+\frac{2}{7}+\frac{5}{7}\right)=\frac{1}{7}.7=1\)
\(c,3.136.8+4.14.6-14.150=3264+336-2100=1500\)
\(d,\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{110}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{10.11}\)\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)\(=\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\)
\(e,\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{37.39}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{37}-\frac{1}{39}=\frac{1}{3}-\frac{1}{39}=\frac{4}{13}\)
31 tháng 5 2017
c) x=-2 nha
d) =\(\frac{1}{5.6}\)+\(\frac{1}{6.7}\)+......+\(\frac{1}{11.12}\)
=\(\frac{1}{5}\)-\(\frac{1}{6}\)+\(\frac{1}{6}\)-\(\frac{1}{7}\)+.....+\(\frac{1}{11}\)-\(\frac{1}{12}\)
=\(\frac{1}{5}\)-\(\frac{1}{12}\)= \(\frac{7}{60}\)
5 tháng 4 2017
ta gọi \(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{90}\)là A
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(\Leftrightarrow1.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{9}-\frac{1}{10}\right)\)
\(\Rightarrow A=1-\frac{1}{10}=\frac{9}{10}\)
ta gọi B là biểu thức thứ2
\(B=\frac{2.2}{3}\times\frac{3.3}{2.4}\times\frac{4.4}{3.5}\times...\times\frac{10.10}{9.11}\)
\(\Rightarrow\)2 x \(\frac{10}{11}\)\(=\frac{20}{11}\)
\(\Rightarrow\)\(x+\frac{9}{10}=\frac{20}{11}+\frac{9}{110}\)
\(\Rightarrow x=1\)
mk nghĩ vậy bạn ạ, mk mong nó đúng
\(\left(\times-\frac{1}{5}\right):\left(\frac{1}{2}+\frac{1}{6}+\cdot\cdot\cdot+\frac{1}{110}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(\frac{1}{1\times2}+\cdot\cdot\cdot+\frac{1}{10\times11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(1-\frac{1}{2}+\cdot\cdot\cdot+\frac{1}{10}-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(1-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right):\frac{10}{11}=\frac{1}{5}\)
\(\Rightarrow\left(\times-\frac{1}{5}\right)=\frac{1}{5}\times\frac{10}{11}\)
\(\Rightarrow\times-\frac{1}{5}=\frac{2}{11}\)
\(\Rightarrow\times=\frac{2}{11}+\frac{1}{5}\)
\(\Rightarrow\times=\frac{21}{55}\)
\(\left(x-\frac{1}{5}\right):\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{10\times11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\left(1-\frac{1}{11}\right)=\frac{1}{5}\)
\(\Rightarrow\left(x-\frac{1}{5}\right):\frac{10}{11}=\frac{1}{5}\)
\(\Rightarrow x-\frac{1}{5}=\frac{1}{5}\times\frac{10}{11}\)
\(\Rightarrow x-\frac{1}{5}=\frac{2}{11}\)
\(\Rightarrow x=\frac{2}{11}+\frac{1}{5}\)
\(\Rightarrow x=\frac{21}{55}\)
Vậy \(x=\frac{21}{55}\)