Introduction to sequences

Intros
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Lessons
  1. Notation of Sequences
  2. Definitions and theorems of Sequences
Examples
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Lessons
  1. Finding the terms of a sequence

    Find the first five terms of the following sequences.
    1. an=3(−1)n a_n=3(-1)^n
    2. ana_n= n+1n+1\frac{n+1}{\sqrt{n+1}}
    3. {cos(nπ2) cos(\frac{n\pi}{2}) }
  2. Finding the formula for a sequence

    Find the formula for the general term ana_n for the following sequences
    1. {12,13,14,15,... \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, ... }
    2. {12,25,38,411,... \frac{1}{2}, \frac{2}{5}, \frac{3}{8}, \frac{4}{11}, ... }
    3. {-1, 4, -9, 16, ... }
  3. Convergence and divergence of sequences

    Evaluate the limits and determine if the following limits are converging or diverging.
    1. lim⁡\limn →∞\infty (−1)nn2\frac{(-1)^n}{n^2}
    2. lim⁡\limn →∞\infty 6(12)n6(\frac{1}{2})^n
    3. lim⁡\limn →∞\infty n3+n+1n2+1\frac{n^3+n+1}{n^2+1}