\(N=\frac{1}{1x5}+\frac{1}{5x10}+...+\frac{1}{2005x2010}\)
\(\Rightarrow5N=\frac{5}{1x5}+\frac{5}{5x10}+\frac{5}{10x15}+...+\frac{5}{2005x2010}\)
\(\Rightarrow5N=1-\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{2005}-\frac{1}{2010}\)
\(\Rightarrow5N=1-\frac{1}{5}-\frac{1}{2010}\)
\(\Rightarrow5N=\frac{4}{5}-\frac{1}{2010}\)
\(\Rightarrow5N=\frac{1607}{2010}\)
\(\Rightarrow N=\frac{1607}{10050}\)
Nhấn đúng cho mk nha!!!!!!!!!
\(=\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+..........+\frac{1}{2005}-\frac{1}{2010}\)
\(=\frac{1}{1}-\frac{1}{2010}\)
\(=\frac{2009}{2010}\)