\(N=\frac{1}{1.5}+\frac{1}{5.10}+...+\frac{1}{2005.2010}=\frac{1}{5}\left(\frac{5}{1.5}+\frac{5}{5.10}+...+\frac{5}{2005.2010}\right)=\frac{1}{5}\left(\frac{1}{1}-\frac{1}{5}+...+\frac{1}{2005}-\frac{1}{2010}\right)\)
\(N=\frac{1}{5}.\frac{2009}{2010}=\frac{2009}{2010}\)
Bài bạn Mạnh Chưa đúng. bạn Hạnh kiểm tra lại nhé
\(N=\frac{1}{1.5}+\frac{1}{5.10}+....+\frac{1}{2005.2010}\)
\(N=5.\left(\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+....+\frac{1}{2005}-\frac{1}{2010}\right)\)
\(N=5.\left(\frac{1}{1}-\frac{1}{2010}\right)\)
\(N=5.\frac{2009}{2010}\)
\(N=\frac{2009}{402}\)
\(N=\frac{1}{1.5}+\frac{1}{5.10}+\frac{1}{10.15}+...+\frac{1}{2005.2010}\)
\(4N=\frac{4}{1.5}+\frac{4}{5.10}+\frac{4}{10.15}+...+\frac{4}{2005.2010}\)
\(4N=\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{2005}-\frac{1}{2010}\)
\(4N=1-\frac{1}{2010}\)
\(4N=\frac{2010-1}{2010}\)
\(N=\frac{2010-1}{8040}=\frac{2009}{8040}\)