Several series/1/Exercise

Determine whether the following series converge:

1. ${}\sum _{n=1}^{\infty }{\frac {n+3}{n^{3}-n^{2}-n+2}}$,
2. ${}\sum _{n=1}^{\infty }{\frac {n+{\sqrt {n}}}{n^{2}-{\sqrt {n}}+1}}$,
3. ${}\sum _{n=1}^{\infty }(-1)^{n}({\sqrt {n}}-{\sqrt {n-1}})$.

Create a solution