Explore advanced calculus concepts in this comprehensive video lecture on strategies for testing series convergence. Learn to apply various tests including Direct Comparison Test, Root Test, Test for Divergence, Alternating Series Test, Ratio Test, Limit Comparison Test, and Integral Test. Analyze complex series such as 1/(n+3^n), (2n+1)^n/(n^(2n)), and n^2*e^(-n^3). Master techniques for determining convergence or divergence of infinite series, with practical examples and step-by-step solutions. Gain proficiency in handling alternating series, absolute convergence, and challenging problems involving factorials and exponential functions.
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
