求下面的极限

永远

\[\mathop {\lim }\limits_{n \to \infty } \sum\limits_{m = 0}^\infty  {\frac{{\Gamma (\frac{1}{{2n}} + 1)}}{{\Gamma (m + 1)\Gamma (\frac{1}{{2n}} - m + 1)}}} {( - 1)^m}\frac{1}{{2nm + 1}}\]