Content:

Applet

Theory

Analysis for Computer Scientists, Chapter 5

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### Entering a sequence

The sequence is defined in the field a(n)=, see the screenshot. Two methods of input are accepted:

• The sequence is given explicitly. In this case a formula in the single variable n must be entered, for example, 2*n^3-n/2. Then the Initial index and Final index must be entered in the appropriate fields. Since the sequence is given explicitly no initial value is required and the corresponding field Initial value must remain empty.
• The sequence is given recursively. In this case a recursion formula in terms of a(n-1),a(n-2),...,a(n-k) must be entered. The length of the recursion is arbitrary (at least in principle). Note that the corresponding number of initial values must be entered. In the screenshot the recursion 3.99*a(n-1)*(1-a(n-1)) is displayed. In this example, a single value must be entered into the field Initial value. In the case of multiple initial values (as e.g. for the Fibonacci sequence), these values must by separated by a comma.

Detailed information on the input format of functions can be found here. The combo box Load sequence can be used to load a number of examples. These examples also serve to illustrate the input format explained above. ### Plotting a sequence

By pressing the button Compute the terms of the sequence are computed and the corresponding graph is drawn. The graph consists of the points (n,a(n)) marked as red dots. For better visualisation two consecutive points are connected by a blue line. To display the value of a term of the sequence, the cursor must be placed at the corresponding point in the graph. In addition, by pointing at the first or last element of the sequence the defining formula is displayed.

### Plotting multiple sequences

If the option Draw sequences separately is disabled, all entered sequences will be displayed in the same window.

### Error messages

The text field at the lower boundary of the applet informs you about errors in the input syntax (e.g. syntax error in the formula, wrong number of initial values) and errors that have occured while computing the sequence (e.g. overflow, division by zero).

### Questions

If you have further questions or comments, or if you found a bug, please send us an e-mail.

Financially supported by

University of Innsbruck: New Media and Learning Technologies
Austrian Federal Ministry of Education, Science and Research

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