[tex]( \frac{1}{1} - \frac{1}{3}+ \frac{1}{3} - \frac{1}{5}+...+ \frac{1}{2013} - \frac{1}{2015} )* \frac{2015}{2014}= \\ =(se. reduc. termenii. asemenea)( \frac{1}{1} - \frac{1}{2015}) * \frac{2015}{2014}= \frac{2014}{2015}* \frac{2015}{2014}=1 [/tex]