Question

va rog pls repede !!!

Answer 1

[tex] \frac{4}{1*5} + \frac{4}{5*9} + \frac{4}{9*13} +...+ \frac{4}{2013*2017}= \\ = \frac{5-1}{1*5} + \frac{9-5}{5*9} + \frac{13-9}{9*13} +...+ \frac{2017-2013}{2013*2017} = \\ = \frac{5}{1*5} -\frac{1}{1*5} + \frac{9}{5*9} - \frac{5}{5*9} +\frac{13}{9*13}-\frac{9}{9*13}+...+ \frac{2017}{2013*2017} - \frac{2013}{2013*2017} = \\ = \frac{1}{1} - \frac{1}{5} + \frac{1}{5} - \frac{1}{9} + \frac{1}{9} +...+ \frac{1}{2013} -\frac{1}{2017} = \\ = \frac{1}{1} - \frac{1}{2017} = \frac{2016}{2017} [/tex]