In mathematics, the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series. For a non-increasing ... Estimate · Integral comparison · Examples |
| Телескопический признак |  |
Телескопический признак — признак сходимости числовых рядов с положительными членами, установленный Огюстеном Коши в 1821 году. Википедия
1 Cauchy Condensation Test. Theorem 1.1. Suppose a1 ≥ a2 ≥ a3 ≥ a4 ≥···≥ 0. Then. ∞. ∑ n=1 an converges if and only if. ∞. ∑ k=0. 2ka2k = a1 + 2a2 + 4a4 ... |
The following test for convergence is known as the Cauchy Condensation Test. It applies to series with nonnegative, decreasing terms. Theorem. |
The main purpose of the Cauchy Condensation test is to prove that the p-series converges if p > 1. |
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Comparison test determines the convergence or the divergence of a series by comparing it to the one whose behavior is already known. Theorem 13.2 (Comparison ... |
The Cauchy Condensation Test is a method used to test the convergence of a series. It involves taking a sum over the terms of the series where the index is ... |
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