Question

calculati 1+1/2+1/3+1/4+1/5+.....................1/2005+1/2+2/3+3/4+...............2004/2005

Answer 1

$1+ \frac{1}{2}+ \frac{1}{3}+...+ \frac{1}{2005} + \frac{1}{2} + \frac{2}{3} + \frac{3}{4} +...+\frac{2004}{2005} = \\ =1+( \frac{1}{2}+ \frac{1}{2} )+( \frac{1}{3}+ \frac{2}{3})+...+( \frac{1}{2005}+ \frac{2004}{2005})= \\ =1+1+1+...+1 (2005.termeni)= \\ =2005$