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HV
1
HV
1
HN
9 tháng 1 2022
\( \begin{array}{l} \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{6} +\frac{1}{12} +\frac{1}{20} +...+\frac{1}{240}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2.3} +\frac{1}{3.4} +\frac{1}{4.5} +...+\frac{1}{15.16}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{3} +\frac{1}{3} -\frac{1}{4} +...+\frac{1}{15} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\frac{7}{16}\\ \Leftrightarrow \ B=\frac{7}{32} \end{array}\)
HV
1
HN
9 tháng 1 2022
\( \begin{array}{l} \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{6} +\frac{1}{12} +\frac{1}{20} +...+\frac{1}{240}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2.3} +\frac{1}{3.4} +\frac{1}{4.5} +...+\frac{1}{15.16}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{3} +\frac{1}{3} -\frac{1}{4} +...+\frac{1}{15} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\frac{7}{16}\\ \Leftrightarrow \ B=\frac{7}{32} \end{array}\)
NK
0
PG
3
XO
27 tháng 10 2019
K = \(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}+\frac{1}{112}\)
\(=\frac{1}{2}\times\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{8}\right)\)
\(=\frac{1}{2}\times\frac{7}{8}=\frac{7}{16}\)
8 tháng 7 2018
\(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}\)
\(=\frac{1}{2}\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{7}\right)\)
\(=\frac{1}{2}.\frac{6}{7}=\frac{3}{7}\)
8 tháng 7 2018
Đặt \(C=\frac{1}{2}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{84}\)
\(\Rightarrow\frac{C}{2}=1+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{42}\)
\(\Rightarrow C.\frac{1}{2}=1+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{6.7}\)
\(\Rightarrow C.\frac{1}{2}=1+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)
\(\Rightarrow C.\frac{1}{2}=1+\frac{1}{2}-\frac{1}{7}\)
\(\Rightarrow C=\left(1+\frac{1}{2}-\frac{1}{7}\right).2\)
HH
3