This applet shows the relationship between terms of a sequence and the partial sums of a series. It also allows exploration of some important sequences and the corresponding series.
Type of Material:
Simulation
Recommended Uses:
This site can be used for a self-study or individual student practice. It is also possible to use this tool as an aid for in-class demonstration.
Technical Requirements:
Any browser
Identify Major Learning Goals:
Develop a better understanding of the concepts of infinite sequences and series.
Target Student Population:
Students in a Calculus course.
Prerequisite Knowledge or Skills:
Second semester of Calculus.
Content Quality
Rating:
Strengths:
This site allows the user to visually explore the definition and basic properties of the infinite sequences and series. The user could choose from a selection of several standard sequences and afterwards the graph of the sequence’s terms and the partial sums of the series is displayed. The list of terms and partial sums is also displayed on a spreadsheet to the right. Alternatively, one can type in the user’s own formula for the n-th term. The tool can also display limit values for the preset formulas. A convenient slider control allows changing the total number of points displayed. The zoom feature of the tool is very helpful.
Concerns:
The site does not contain rigorous definitions of sequences or series nor does it contain proper references. When the number of terms exceeds 100, the graph displays correctly, but the spreadsheet stops at 100.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The site can be used as a part of in-class demonstration or a self-guided activity. An instructor can also assign take home exercises that would require students to use this tool. It is especially effective for the kinesthetic learner.
Concerns:
None
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The tool is very user friendly and intuitive. Anybody can start using it right away. It has basic instructions at the bottom which include explorative questions about the limit of the sequence and the limit of the series.
Concerns:
None
Creative Commons:
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