AP Calculus Series—— Absolute and Conditional Convergence中国试卷网
2016.03.17
1. Absolute and Conditional Convergence
a) The ries converges absolutely if converges.
b) An infinite ries converges conditionally if converges but instagram是什么意思diverges.
c) If converges, then also converges.
2. Alternating Series The ries who terms are alternately positive and negative is called alternating ries, for example.
editorial3. Leibniz Test for Alternating Series Assume that hsyis a positive quence that is decreasing and converges to 0: .
Then the following alternating ries converges:
Furthermore， and takeup.
Let , where is a positive decreasing quence that converges to 0. Then .In other words, the error committed when we approximate by is less than the size of the first omitted term .
4. Ratio Test
Assume that the following limit exists:
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a) If , then converges absolutely.
b) If tinman, then diverges.
c) If valentines, then the test is inconclusive (the ries may converge or diverge).
5. Root Test
Assume that the following limit exists:
a) If , then converges absolutely.
b) If , then diverges.
c) If , then the test is inconclusive (the ries may converge or diverge).
Exerci
1. U the Ratio Test to determine whether the infinite ries is convergent.
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2. U the Root Test to determine whether the infinite ries is convergent.
