Question: Determine whether

(i) \(\sum\limits_{n=1}^{\infty }{\frac{n+1}{3{{n}^{2}}+3n+2}}\)

(ii) \(\sum\limits_{n=1}^{\infty }{\frac{{{n}^{n}}}{n!}}\)

(iii) \(\sum\limits_{n=1}^{\infty }{\frac{{{x}^{n}}}{{{n}^{2}}}}\), with \(x\in R\)