[tex]\it x+y= \Big(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\ ...\ +\dfrac{1}{10}\Big)+\Big(\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+\ ...\ +\dfrac{9}{10}\Big)=\\ \\ \\ =\Big(\dfrac{1}{2}+\dfrac{1}{2}\Big)+\Big(\dfrac{1}{3}+\dfrac{2}{3}\Big)+\Big(\dfrac{1}{4}+\dfrac{3}{4}\Big)+\ ...\ +\Big(\dfrac{1}{10}+\dfrac{9}{10}\Big)=\\ \\ \\ =\underbrace{1+1+1+\ ...\ +1}_{9\ termeni}=9[/tex]
