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Video 12 - Summation Notation, Infinite Series, Integral Test.
- Summation Notation.
The sigma notation for summation is reviewed, examples are worked showing how to compute sums expressed in sigma notation. The concept of dummy index is discussed and examples are worked showing how to change indices in the sigma notation via substitution.
- Infinite Series.
The basic definitions of infinite series and partial sums are reviewed, the definitions of convergence and divergence for infinite series are reviewed and the nth term test for divergence of an infinite series is reviewed. Examples of telescoping series and geometric series are worked as well as examples showing the use of the nth term test to prove divergence of certain series.
- Comparison Test.
The comparison test and limit comparison tests are reviewed and discussed for infinite series and examples are worked illustrating their use in determining convergence or divergence of certain infinite series.
- Integral Test.
The comparison test and limit comparison tests are reviewed and discussed for infinite series and examples are worked illustrating their use in determining convergence or divergence of certain infinite series.
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