[tex] \frac{1}{1+ \sqrt{2}} + \frac{1}{ \sqrt{2}+ \sqrt{3}} + \frac{1}{ \sqrt{3} +2} [/tex]
Amplificam fiecare fractie cu conjugatul numitorului, si obtinem:
[tex] \frac{1- \sqrt{2} }{1-2}+ \frac{ \sqrt{2}- \sqrt{3} }{2-3}+ \frac{ \sqrt{3}-2 }{3-4}= [/tex]
[tex] \frac{1- \sqrt{2}+ \sqrt{2}- \sqrt{3} + \sqrt{3} -2}{-1}= \frac{1-2}{-1} = \frac{-1}{-1} = 1 [/tex]
1 ∈ lN
cctd
