Any help/hints for any of these exercises would be much appreciated!

**3.** $\displaystyle \sum(-1)^n\binom{2n}{n}x^n$ has a radius of convergence of $\displaystyle \frac{1}{4}$. Determine whether or not each endpoint converges.

**4.** $\displaystyle \sum\frac{n^n}{n!}x^n$ has a radius of convergence of $\displaystyle \frac{1}{e}$. Determine whether or not each endpoint converges.

**5.** $\displaystyle \sum\frac{\alpha(\alpha+1)\cdots(\alpha+n-1)}{\beta(\beta+1)\cdots(\beta+n-1)}x^n$ (with $\displaystyle \alpha,\beta\neq$ negative integer) has a radius of convergence of $\displaystyle 1$. Determine whether or not each endpoint converges.

Determining the radiuses of convergence for these series was easy, but I don't seem to have enough tools in my toolbox of math tricks to routinely solve the endpoints. I am therefore looking to learn new tricks! Please share them if you've got them.

Thanks!

EDIT: The following have been solved:

**1.** $\displaystyle \sum\left(1+\frac{1}{n}\right)^{n^2}[2+(-1)^n]^nx^n$ has a radius of convergence of $\displaystyle \frac{1}{3e}$. Determine whether or not each endpoint converges.

**2.** $\displaystyle \sum\left(2+\sin\frac{n\pi}{6}\right)^nx^n$ has a radius of convergence of $\displaystyle \frac{1}{3}$. Determine whether or not each endpoint converges.