This course covers strategies for testing series in calculus, focusing on determining convergence or divergence of infinite series. The course teaches various tests including the Direct Comparison Test, Root Test, Alternating Series Test, Ratio Test, Limit Comparison Test, Integral Test, and more. The teaching method involves presenting different series problems and explaining the application of each test. This course is intended for students studying calculus who want to deepen their understanding of series testing methods.
Overview
Syllabus
11.7#1, Series 1/(n+3^n), Direct Comparison Test DCT.
11 7#2 Root Test, Series (2n+1)^n/(n^(2n)).
11 7#3 Test for Divergence (for an Alternating Series), Series (-1)^n*n/(n+2).
11.7#4 Alternating Series Test.
11.7#5 Ratio Test.
11.7#6, Limit Comparison Test, Series 1/(2n+1).
11.7#7 integral test, Series 1/(n*sqrt(ln(n))).
11 7#8 Ratio Test, series (2^k*k!)/(k+2)!.
11 7#8 Test for Divergence, series (2^k*k!)/(k+2)!.
11.7#9 Ratio Test.
11.7#10 Integral Test, with Klay Thompson, Series n^2*e^(-n^3).
Series 1/n^3, Series 1/3^n.
11 7#12 blue & yellow chalks? Direct Comparison Test (Short Solution).
11 7#12 Both LCT and DCT.
11.7#13 Ratio Test, Series 3^n*n^2/n!.
11 7#14 Checking for Absolute Convergence.
11.7#16 Both LCT and DCT.
11 7#25 Ratio Test, series n!/e^(n^2).
11 7#37 Root Test, Series (2^(1/n)-1)^n.
11 7#38 Limit Comparison Test, Series (2^(1/n)-1).
Taught by
blackpenredpen
