How to test for convergence

In this blog post, we will be discussing How to test for convergence.

Series Convergence Tests

Activity: Series Converging to π π and 1 π 1 π The series π =4 ∞ ∑ n=1 (−1)n+1 2n−1 = 4 − 4 3 + 4 5 − 4 7 + 4 9 −⋯ π = 4 ∑ n = 1 ∞ ( − 1) n + 1 2 n − 1 = 4 − 4 3 + 4 5 Prove that this series

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Calculus II

This test involves choosing a sufficient series for which you know the convergence/divergence of, and compares it to a series through a limit. This test is often used

3.3 Convergence Tests for Infinite Series

However, use a different test to determine the convergence or divergence of a series. Example 1: Using the Test for Divergence. Show that the series ∑ n = 1 ∞ [n 2] / [5n 2
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Series Convergence Tests

This leads us to the first of many tests for the convergence/divergence of a series that we’ll be seeing in this chapter. Divergence Test If lim n→∞ an ≠ 0 lim n → ∞ a n ≠ 0 then

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Summary of Convergence Tests

Alternating Series Test. If (i) n +1. ≤. b. n. for all n and (ii) lim =0 →. ∞. n n. b, then . ∑. ∞ = − −. 1 ( 1) 1. n n. b. is convergent. The following 2 tests prove convergence, but also prove the stronger

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