28:00 I thought that the original series only converges if the absolute value converges. In this example, we used ratio test which already uses the absolute value of the series, and then we concluded that the absolute value of the series diverges. But wouldn't we still need to check the original series for conditional convergence or absolute divergence? Based on the rules you wrote down here at 0:01
Ratio and Root Tests are “all or nothing” as I like to call them-when using those tests either the series converges absolutely or diverges, no in between so no need to check for conditional convergence.
you are such a great teacher with great teaching skill.
Thank you so much 🥹🫶🏻
Professor V is on the case! Yay! ❤😊
Yes indeed!!! 🥰🙌🏻 (That reminds me of Paw Patrol, “Chase is on the case!”, my nephew’s current obsession 🤣)
God bless Professor V, your explaining is out of this world♥🙏
Thank you so much-that means the world to me! ☺️☺️🫶🏻🥹
28:00 I thought that the original series only converges if the absolute value converges. In this example, we used ratio test which already uses the absolute value of the series, and then we concluded that the absolute value of the series diverges. But wouldn't we still need to check the original series for conditional convergence or absolute divergence? Based on the rules you wrote down here at 0:01
Ratio and Root Tests are “all or nothing” as I like to call them-when using those tests either the series converges absolutely or diverges, no in between so no need to check for conditional convergence.
You are extremely underrated