Harold’s Series Convergence Tests Cheat Sheet 24 March 2016 1 Divergence or nth Term Test Series: ∑∞ 𝑛 𝑛=1 𝑛 Condition(s) of Convergence: None. This test cannot be used to show convergence. Ὄ Condition(s) of Divergence: 1 lim 𝑛→∞ 𝑛≠0 2 Geometric Series Test Series: ∑∞ 𝑟 𝑛=0 1 Condition of Convergence: |𝑟|<1
For any series X∞ n=0 a n, there are 3 cases: Ratio Test: Calculate lim n→∞ a n+1 a n = L if L < 1, then X∞ n=0 |a n| converges ; Root Test: Calculate lim n→∞ n p |a n| = L if L > 1, then X∞ n=0 |a n| diverges; if L = 1, no conclusion can be made. 2. Important Series to Remember Series How do they look Conclusions Geometric Series ...
SERIES CHEAT SHEET BLAKE FARMAN Lafayette College Tests Theorem (nth Term Test for Divergence). If the sequence fa ngdoes not converge to zero, then the series P a n diverges. WARNING: If lim n!1a n = 0 then the test is inconclusive! Theorem (The Integral Test). Let fa n g1 =1 be a sequence. Assume that there exists an integer N 0 and
Cheat Sheets & Tables - Pauls Online Math Notes
2018年9月25日 · Here is list of cheat sheets and tables that I've written. All of the cheat sheets come in two version. A full sized version and a "reduced" version.
Check the convergence of a series X an by the following steps. Check that lim = 0. If not the series diverges. Check X X janj by any test. If this converges an is absolutely convergent. X Note: If you apply the the ratio or root test to janj and get a limiting ratio r > 1, the series diverges and Step (3) is not needed.
Try one or more of the following tests: NO COMPARISON TEST Pick {bn}. Does P bn converge? Is 0 ≤ an ≤ bn? YES P YES an Converges Is 0 ≤ bn ≤ an? NO NO P YES an Diverges LIMIT COMPARISON TEST Pick {bn}. Does lim n→∞ an bn = c > 0 c finite & an,bn > 0? Does X∞ n=1 YES bn converge? P an Converges YES P an Diverges NO INTEGRAL TEST ...
Here’s a list of all of the convergence tests for series that you know so far: Divergence test (a.k.a. n-th term test) Geometric series test Telescoping series Integral test p-series (including harmonic series) Term-size comparison test (also known as \The Comparison Test" or \Direct Comparison Test") Limit comparison test Alternating series test
Positive Series Positive Serie: If all the terms sn are positive. Integral Test: If f(n) = sn, continuous, positive, decreasing: P sn converges R 1 1 f(x)dx converges. Comparison Test: P an and P bn where ak < b k (8k m ) 1. If P bn converges, so does P an 2. If P an diverges, so does P bn Limit Comparison Test: P an and P bn such that lim n !1 ...
Summary of the convergence tests that may appear on the AP Calculus BC exam. The series ... For divergence only; the converse is false. f must be continuous, positive and decreasing. the ratio test cannot be used. Other useful convergence tests that may be used. The series ...
Useful for series containing both positive and negative terms. Alternating series X 1 n =1 ( 1) n 1 a n ( a n > 0) Converges if 0 < a n +1 < a n for all n and lim n !1 a n = 0 Applicable only to series with alternating terms. *The Root and Limit Comparison tests are not included in the current textbook used in Calculus classes at Bates College. 1