Section 10.2 : More on Sequences
For each of the following problems determine if the sequence is increasing, decreasing, not monotonic, bounded below, bounded above and/or bounded.
- \(\left\{ {\displaystyle \frac{1}{{{n^3} + 1}}} \right\}_{n = 1}^\infty \)
- \(\left\{ {{{\bf{e}}^{3n}}} \right\}_{n = 0}^\infty \)
- \(\left\{ {{{\left( { - 3} \right)}^n}} \right\}_{n = 0}^\infty \)
- \(\left\{ {\sin \left( n \right)} \right\}_{n = 4}^\infty \)
- \(\left\{ {\ln \left( {\displaystyle \frac{1}{n}} \right)} \right\}_{n = 2}^\infty \)
- \(\left\{ {\displaystyle \frac{{3 - n}}{{1 - 3n}}} \right\}_{n = 1}^\infty \)
- \(\left\{ {\displaystyle \frac{{2n + 1}}{{4n + 3}}} \right\}_{n = 0}^\infty \)
- \(\left\{ {\left( {1 - n} \right){{\bf{e}}^n}} \right\}_{n = 3}^\infty \)
- \(\left\{ {\displaystyle \frac{{{n^2} + 40}}{{{n^2} + 3n + 1}}} \right\}_{n = 1}^\infty \)
- \(\left\{ {\displaystyle \frac{{5 + n}}{{100,000 + {n^2}}}} \right\}_{n = 0}^\infty \)