${{\int }_0}^1 e^{-X^{2 }} dx=?$

$\sum _{k=0}^{\infty }\frac{(-1{)}^{k } x^{2k}}{2^{2k}(k!{)}^2}$

$\sum _{k=0}^{\infty }\frac{(-1{)}^{k } }{(2k+1)k!}$

$\sum _{k=0}^{\infty }\frac{(-1{)}^{k } \ln x }{\sqrt{k} k!}$

$\sum _{k=0}^{\infty }\frac{(-1{)}^{k +1} x{ }^k}{ k!}$

$\sum _{k=0}^{\infty }\frac{(-1{)}^{k } x{ }^{-{\displaystyle \frac{1}{2}}}}{ 2\ln k}$