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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

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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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.