Ta có:\(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2009.2011}\)
\(2A=2.\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2009.2011}\right)=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2009.2011}\)
\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2009}-\frac{1}{2011}\)
\(=1-\frac{1}{2011}=\frac{2010}{2011}\)
=>\(A=\frac{2010}{2011}:2=\frac{2010}{2011}.\frac{1}{2}=\frac{1005}{2011}\)
Tính : \(\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}...+\frac{1}{2009\times2011}\)
Tính nhanh : \(\frac{1}{1\times3\times5}+\frac{1}{3\times5\times7}+\frac{1}{5\times7\times9}+.....+\frac{1}{45\times47\times49}\) Help me . Mình cần gấp , HELP
\(\frac{7}{1\times3}+\frac{7}{3\times5}+\frac{7}{5\times7}+......+\frac{7}{99\times101}\)
Giúp mình với!!!!!
Tính:
G=\(\frac{1}{1\times3\times5}+\frac{1}{5\times7\times9}+\frac{1}{9\times11\times13}+...+\frac{1}{49\times51\times53}\)
\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+\frac{1}{8\times9}+\frac{1}{9\times10}\)
chứng tỏ:\(\frac{36}{1\times3\times5}+\frac{36}{3\times5\times7}+.....+\frac{36}{25\times27\times29}\)lớn hơn 3
Các bạn giúp mk, mk cần gấp!
\(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+......+\frac{4}{99\times101}\)
\(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+...+\frac{4}{2011\times2013}\)
\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+.....+\frac{2}{x\times\left(x+2\right)}=\frac{2015}{2016}\)
