Pou�it� Abelovy v�ty je v po��dku. 
$$
1-{\frac {1\,x^2}{2}}+{\frac {1\,3\,x^4}{2\,4}}
-{\frac {1\,3\,5\,x^6}{2\,4\,6}}
+ \cdots
$$
konverguje pro $x=1$. Tedy
$$
1-{\frac {1}{2}}+{\frac {1\,3}{2\,4}}
-{\frac {1\,3\,5}{2\,4\,6}}
+ \cdots = 
\lim _{x\rightarrow 1 -}{\frac {1}{\sqrt {1+{x}^{2}}}
}={\frac {\sqrt {2}}{2}} \quad .
$$