Question: Evaluate the limit (if it exists) of each of the following sequences. Indicate the results (definitions, theorems, etc.) you use to support your conclusions

a ) \({{a}_{n}}={{\left( \frac{n-3}{n} \right)}^{n}}\)

b) \({{a}_{n}}=\frac{{{\left( n! \right)}^{2}}}{\left( 2n \right)!}\)

c) \({{a}_{n}}=\frac{{{n}^{2}}{{2}^{n}}}{n!}\)

d) \(\left\{ \frac{1}{{{3}^{n}}},-\frac{1}{{{3}^{6}}},\frac{1}{{{3}^{7}}},-\frac{1}{{{3}^{8}}},.... \right\}\)

e) \({{a}_{n}}=\sqrt{{{n}^{2}}+3n}-n\)

f) \({{a}_{n}}=\frac{{{\left( -1 \right)}^{n}}2{{n}^{3}}}{{{n}^{3}}+1}\)