Question

1/1*2+1/2*3+1/3*4+...+1/2013*2014

Answer 1

[tex] \frac{1}{1*2}+ \frac{1}{2*3}+ \frac{1}{3*4}+...+ \frac{1}{2013*2014}= \\ = \frac{1}{1}- \frac{1}{2} + \frac{1}{2}-\frac{1}{3}+ \frac{1}{3}-\frac{1}{4}+...+ \frac{1}{2013}-\frac{1}{2014}= \\ = \frac{1}{1}-\frac{1}{2014}= \\ = \frac{2014}{2014}-\frac{1}{2014}= \\ = \frac{2014-1}{2014}= \\ = \frac{2013}{2014}[/tex]