Question: Determine whether the following sequences are (eventually) decreasing, (eventually) increasing, or neither. Explain.

a) \(\left\{ 4-\frac{{{\left( -1 \right)}^{n}}}{n} \right\}\)

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

c) \(\left\{ \frac{{{n}^{2}}{{2}^{n}}}{n!} \right\}\)

d) \(\frac{{}}{{}}\) \(\frac{1\cdot 3\cdot 5\cdot \cdot \cdot \left( 2n-1 \right)}{{{\left( 2n \right)}^{n}}}\)