Wednesday, June 12, 2013

The Art of Convergence Tests

Infinite series can be very useful for computation and problem solving but it is often one of the most difficult concepts in calculus. There are several ways of testing a series for convergence or divergence; the problem is to decide which test to use on which series. The p series test, geometric series test, telescoping series test, root test, ratio test, integral test, alternating series test, comparison test, divergence test to name a few. Testing series is similar to integration, you need a strategy to begin with.


Strategy?  You guessed right, Symbolab can help you with that; the art of conversion test. Simply type in the series using the pad (or Latex), press Go, and … you get the convergence test with detailed steps, just like that!

In fact our algorithms automatically choose and execute the best convergence test, but that’s for a different blog post, or not…

We are also introducing yet another super cool feature, the interim steps.  Most of the convergence tests like the Ratio test, Comparison test, divergence test or the Integral test involve complex limit or integral calculations.    The comparison test for instance involves choosing a series, the interim steps will remind you how to test the series you've chosen for convergence or divergence and what the test is all about.

Take a look at these examples to get started:
Limit Comparison Test:


Click the gray plus for the test specifications


Click the red plus for interim steps, in this example the series and limit steps:


Click the gray plus in the box for more information on Cauchy’s condition:


Some more examples:
Alternating Series Test example:


Integral Test Example:


Ratio Test Example:


We hope you find these new features exciting and helpful.
Stay tuned for more updates.

Cheers,
Michal

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