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Question
Pls sir, it's my 1st time to hear of convergence and divergence test and my exam is just 2weeks away, can you please help me with any shortcuts for answering questions on convergence and divergence. Thanks in advance

Answer
A divergent series is one where as n increases, the series goes to plus or minus infinity.
Examples with n as the variable that goes to infinity would be -n/5, n/ln(n), or (-1.1)^n

A convergent series would be one that had a limit it approached.
Examples would be (1/2)^2, (-1)^n/n^2, or ln(1/n).

An easy shortcut is cancelling any terms and seeing if that makes it apparent.

Another shortcut is taking the absolute value of the top and bottom.
If this converges, the sequence converges.

If the top and bottom of the fraction both go to 0 or both go to infinity,
take the derivative of the top over the derivative of the bottom
and see what that does.

A good place to look for tests is tutorial.math.lamar.edu/Classes/CalcII/SeriesIntro.aspx

Some tests are the integral test, comparison test, alternating series test,
absolute convergence, ratio test, root test,  etc.

As I understand it, a series is the individual terms and a sequence is the sum of the terms.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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