Explore advanced calculus concepts in this 30-minute video focusing on the Ratio and Root Tests for series convergence. Learn how to apply the Ratio Test to various series, including cases where the Direct Comparison Test (DCT) is not applicable. Examine the Root Test for series involving expressions like (1+1/n)^(n^2) and (1-1/n)^(n^2). Investigate the divergence of the series (1+1/n)^n and apply the Ratio Test to analyze the series n!/n^n. Gain a deeper understanding of these crucial tools for determining series convergence and divergence in calculus.
Overview
Syllabus
Calculus, 11 6 #3, Ratio Test.
Calculus, 11 6 #3, Ratio Test DCT wont apply.
Calculus, 11 6 #7, Ratio Test.
THE FACT.
Series of (1+1/n)^(n^2), root test.
Series (1+1/n)^n, test for divergence.
Series of (1-1/n)^(n^2), root test.
Series of n!/n^n, ratio test.
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