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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.

  1. \(\left\{ {\displaystyle \frac{1}{{4n}}} \right\}_{n = 1}^\infty \) Solution
  2. \(\left\{ {n{{\left( { - 1} \right)}^{n + 2}}} \right\}_{n = 0}^\infty \) Solution
  3. \(\left\{ {{3^{ - \,n}}} \right\}_{n = 0}^\infty \) Solution
  4. \(\left\{ {\displaystyle \frac{{2{n^2} - 1}}{n}} \right\}_{n = 2}^\infty \) Solution
  5. \(\left\{ {\displaystyle \frac{{4 - n}}{{2n + 3}}} \right\}_{n = 1}^\infty \) Solution
  6. \(\left\{ {\displaystyle \frac{{ - n}}{{{n^2} + 25}}} \right\}_{n = 2}^\infty \) Solution