A = 1/1.3 + 1/3.5 + 1/5.7 + ... + 1/2011.2013
A = 1/2.(2/1.3 + 2/3.5 + 2/5.7 + ... + 2/2011.2013)
A = 1/2.(1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/2011 - 1/2013)
A = 1/2.(1 - 1/2013)
A = 1/2.2012/2013
A = 1006/2013
\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2011.2013}\)
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2011.2013}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2011}-\frac{1}{2013}\)
\(2A=1+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+...+\left(\frac{1}{2011}-\frac{1}{2011}\right)-\frac{1}{2013}\)
\(2A=1-\frac{1}{2013}\)
\(2A=\frac{2012}{2013}\)
\(A=\frac{2012}{2013}:2\)
\(A=\frac{1006}{2013}\)
~ Hok tốt ~
\(2A=2\left(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+...+\frac{1}{2011\cdot2013}\right)\)
\(=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{2011\cdot2013}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2011}-\frac{1}{2013}\)
\(=1-\frac{1}{2013}\)
\(=\frac{2012}{2013}\)
\(A=\frac{2012}{2013}\div2=\frac{2012}{2013\cdot2}\)
\(#Louis\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2011}-\frac{1}{2013}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{2013}\right)\)
\(=\frac{1}{2}.\frac{670}{2013}\)
\(=\frac{335}{2013}\)
\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2011.2013}\)
\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2011.2013}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2011}-\frac{1}{2013}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{2013}\right)\)
\(=\frac{1}{2}.\frac{2012}{2013}\)
\(=\frac{1006}{2013}\)
Study well ! >_<
A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2011.2013}\)
= \(\frac{1}{1}-\frac{2}{3}+\frac{2}{3}-\frac{3}{5}+\frac{3}{5}-\frac{4}{7}+...+\frac{1006}{2011}-\frac{1007}{2013}\)
= \(1-\frac{1007}{2013}\)
= \(\frac{2013}{2103}-\frac{1007}{2103}\)
= \(\frac{1006}{2013}\)
