I have some questions about Pade approximants.

1. Given a divergent power series $ \sum\_{n >0} a(n)x^{n} $ can we use a Pade Approximant to it $ R(x)$ so we can obtain a SUM of the series for every $x$ ?
2. Given a Taylor power series $ \sum\_{n >0} c(n)x^{n}=O(x^{a}) $ for positive $x >0$ for some positve but unknown $a$ can we obtain the value of $a$ by approximating the power series by a Pade Approximant?
3. Can we compute a Borel transform of a series $ \sum\_{n>0} \frac{a\_n}{n!}x^{n} $ by a Pade Approximant?
4. Can we use Pade approximation to obtain numerical integration of series and integrals ?