Monotonic and bounded sequences

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Intros
Lessons
  1. Overview:
  2. Monotonic Sequences
  3. Bounded Sequences
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Examples
Lessons
  1. Difference between monotonic and non-monotonic sequences

    Show that the following sequences is monotonic. Is it an increasing or decreasing sequence?
    1. {n2 n^2 }
    2. an=13na_n= \frac{1}{3^n}
    3. {nn+1}n=1 \{\frac{n}{n+1}\}_{n=1}^{\infty}
    4. {1, 1.5, 2, 2.5, 3, 3.5, ...}
  2. Difference between bounded, bounded above, and bounded below

    Determine whether the sequences are bounded below, bounded above, both, or neither
    1. an=n(1)na_n=n(-1)^n
    2. an=(1)nn2a_n=\frac{(-1)^n}{n^2}
    3. an=n3a_n=n^3
    4. an=n4 a_n=-n^4
  3. Convegence of sequences

    Are the following sequences convergent according to theorem 7?
    1. {3n3}n=1 \{\frac{3}{n^3}\}_{n=1}^{\infty}
    2. {(1)2n+12}n=1 \{\frac{(-1)^{2n+1}}{2}\}_{n=1}^{\infty}
    3. {n}n=4 \{\sqrt{n}\}_{n=4}^{\infty}