Explicație pas cu pas:
b)
[tex]\frac{1}{1\cdot 2} + \frac{1}{2 \cdot 3} + ... + \frac{1}{2012 \cdot 2013} + \frac{1}{2013 \cdot 2014} = \\ [/tex]
[tex]= \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{2012} - \frac{1}{2013} + \frac{1}{2013} - \frac{1}{2014} \\ [/tex]
[tex]= \frac{1}{1} - \frac{1}{2014} = \frac{2014-1}{2014} = \red{\bf \frac{2013}{2014}} \\ [/tex]
