Can you do videos on proving why the Ratio and Root tests work as well as why the direct comparison and limit comparison tests work? It’s all fine and dandy to say that if the result of the root test is less than 1, then the original series converges, but how do we know/prove that? Who came up with these tests and why do they work?
First, thank you soo much for your efforts, second i have another idea if you can solve the series with a different ways if it is possible of course ♡♡♡♡♡and thank you for the second time ❤😊
I don't know if you're reading this, but I made 30 timestamps to your 100 series video. I commented under the timestamp comment. Please update! Either way always good practice watching your videos so thank you!
Whenever I see the convergent ones, I always get curious about what they converge to. Most probably won't have closed forms with our current knowledge, but some might.
Timestanps:
Question 1: 0:01
Question 2: 3:49
Question 3: 6:46
Question 4: 9:04
Question 5: 11:49
Question 6: 13:56
Question 7: 16:24
Question 8: 20:22
thank you!
Can you do videos on proving why the Ratio and Root tests work as well as why the direct comparison and limit comparison tests work? It’s all fine and dandy to say that if the result of the root test is less than 1, then the original series converges, but how do we know/prove that? Who came up with these tests and why do they work?
was struggling with a problem similar to #2 with factorial manipulation. Thank you so much for helping!!
You are an actual life saver, thank you!
Thank you so much for this❤
This is very helpful. Thank you !
Thanks very much sir God bless
Such a wonderful video
First, thank you soo much for your efforts, second i have another idea if you can solve the series with a different ways if it is possible of course ♡♡♡♡♡and thank you for the second time ❤😊
How can we find the value that they converge to?
I don't know if you're reading this, but I made 30 timestamps to your 100 series video. I commented under the timestamp comment. Please update!
Either way always good practice watching your videos so thank you!
In problem #6 it was supposed to be a 3 in the top not 3n.
3:48 Why can’t we just do ‘RaT’ for ‘Ratio Test’ and ‘RoT’ for ‘Root Test’?
Because the corresponding words "rat" and "rot" both have negative, gloomy connotations.
@@xinpingdonohoe3978 What are you talking about? Ratrot is my favorite plague in CK3!
Whenever I see the convergent ones, I always get curious about what they converge to. Most probably won't have closed forms with our current knowledge, but some might.
First to comment
This is very helpful. Thank you !