Math 143 Exam #1 Study Guide
Math 143 Exam #1 Study Guide MATH 143
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This 2 page Study Guide was uploaded by Camila Monchini on Monday January 18, 2016. The Study Guide belongs to MATH 143 at California Polytechnic State University San Luis Obispo taught by Robbins in Winter 2016. Since its upload, it has received 56 views. For similar materials see Calculus III in Math at California Polytechnic State University San Luis Obispo.
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Date Created: 01/18/16
What convergence test toa converges or diverges.es n First of all, KNOW THE DIFFERENCE BETWEEN THE SEQUENCE fang AND THE SERIES 1 X an n=1 All of the tests in 10.2-10.6 are tests for conver- gence and/or divergence of series X an: n=1 1 X Choosing a test for convergence and/or divergence of the seriesa n n=1 (1) Is the series geometric or a p-series? If not, ::: (2) Check: If liman6= 0, use the nth term test. If not, ::: (3) Does the alternating series test apply? If so, apply it. If not ::: (4) Are the terms all non-negative? If so, simplify a , then ::: n (a) If n consists of lots of multplication, such as exponential n functions (like 2 ) and factorials try the ratio test. ▯ ▯ n2 7 (b) if n has lots of powers of n (lik1 ▯ n ), try the root test. p (c) ifna is a ratio involving numerical powers of n (like 3n + 3n ), P consider the limit comparison test with dominant term in numerator . dominant in denominator. If not, can you direct compare? (d) Are the terms the sum or di▯erence of terms of series that converge? Test both separately, and then use the algebraic laws of convergent series. (e) Does the integral test apply? (This test is often helpful if there is lnn and 1=n in the term, and none of the previous tests can be applied.) (f) Do the terms look like a sum or di▯erence of terms of two series, one which converges, and one that diverges? Then use the algebraic limit laws. If not ::: (5) If the terms are not all non-negative, but are not alternating signs, try the absolute convergence test.
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