In some organized fashion discuss what order you would use to apply the tests. I
ID: 3345949 • Letter: I
Question
In some organized fashion discuss what order you would use to apply the tests. If this order depends on checking the form of the series, state what you are looking for. For each test, discuss convergence/divergence criteria, and any other interesting features to note. There is not one correct answer. Your ordering may differ from others in the class, and yet both approaches are reasonable. Feel free to discuss your thoughts with your friends, but you need not agree with them on what you turn in.Explanation / Answer
There are many tests, I wil first list them in the order of most used.
1) ratio test
2) comparison test
3) divergence test aka limit test
4) p-series
5) geometric series
6) limit comparison
7) alternating series
8) integral test
9) root test
Basically it all comes down to what the series looks like.
EACH test has certain constraints which tell you if you can use it or not.. You should make a formula sheet with each test and their properties so you can just refer to it back and forth.
For P-series: Basically this is used mostly WITH comparison test and limit comparison test. Becuase when you choose Bn to compare with, many time it will be convergent or divergent with p-series
Use geometric when you have something in the form ar^(n-1)
If you have series with only polynomials use comparison test
ex. (n^2+1) / (n^5+n^2+1) you can use comparison easily and compare with n^2/n^5 which is 1/n^3 which converges
ratio, use when you want to find a radius of convergence or no other test works..
test for divergence: when limit =/= 0 then it converges. very quickly to apply but you can mostly tell you can't use it because the limit will =0 which means it's inconclusive.
integral test: use if the function is postiive decreasing fucntion from [1,inf]
Root test: this is obvious because it's to the power of 1/n
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