To solve this recursion we can use generating functions Ordinary generating function may lead us to ODE but exponential generating function could be better approach
Not sure if that's just me but i hate how maths on youtube is just integrals or olympiad problems, maths is so much more than that, you're definitely qualified enough to delve into more advanced topics so why not do that? Some abstract algebra? Real analysis maybe? Fourier analysis? Topology? There is so much more that can be done instead of those same integrals everyone is doing
Why hate? People are doing it as those are what many people are interested in. Real analysis? Fun but not many of them on TH-cam would be interested in it. They would not do it just because only you are interered in it. And same integrals? They are doing all different integrals
@@iqtrainer It's not hate, it's just that this redundancy isn't doing maths as a topic any favor. Imagine a physics account that only discusses classical mechanics, literally nothing else, and more than that, only pendulum problems!!! They just make the pendulum slightly different everytime!!! Sounds uninteresting and boring right? It's literally the same here
Thats not the same here. Dr PK does integrals, differential equations, advanced algebra, and etc. There are youtube channels that do only integrals. You should leave your comment to those channels, not here. Plus, integrals Dr PK do are all different ones. Not make them slightly different. You are saying that because you are not good at integrals and dont know much of it.
@ Be real. You hate integrals or math olympiad because you are bad at math. Real analysis or topology? if you wanna learn, go learn and stop whining here. No one wants whining from people like you
I guess it is mostly you. I enjoy integrals and also competition maths so much. Integrals and olympiad math questions are the choice from math youtubers. You do not have a right to blame them just because you do not enjoy them. If you like abstract algebra, or real analysis, you just find those channels, and watch the videos. But, once again, you do not have a right to blame anyone
Love especially analytic method to have a nice written expression as an answer
Haha thanks for your support my friend! It's one of my favorites too! 👍👍👍
This one is very interesting professor
Thank you for your support my friend! Haha👍👍👍
Very nice one professor, you are a pro
Thanks a lot my friend haha. Appreciate the support! 👍👍👍
Another great video professor🎉
Thanks a lot my friend 👍👍👍
Nice problem professor
Thanks a lot my friend 👍👍👍
To solve this recursion we can use generating functions
Ordinary generating function may lead us to ODE but exponential generating function could be better approach
Agree, so I prefer method 1 from the video.
Nice to share this my friend👍👍👍
Geometric series expanston and integration by parts
Nice haha thanks for sharing it👍👍👍
Not sure if that's just me but i hate how maths on youtube is just integrals or olympiad problems, maths is so much more than that, you're definitely qualified enough to delve into more advanced topics so why not do that? Some abstract algebra? Real analysis maybe? Fourier analysis? Topology? There is so much more that can be done instead of those same integrals everyone is doing
Why hate? People are doing it as those are what many people are interested in. Real analysis? Fun but not many of them on TH-cam would be interested in it. They would not do it just because only you are interered in it. And same integrals? They are doing all different integrals
@@iqtrainer It's not hate, it's just that this redundancy isn't doing maths as a topic any favor. Imagine a physics account that only discusses classical mechanics, literally nothing else, and more than that, only pendulum problems!!! They just make the pendulum slightly different everytime!!! Sounds uninteresting and boring right? It's literally the same here
Thats not the same here. Dr PK does integrals, differential equations, advanced algebra, and etc. There are youtube channels that do only integrals. You should leave your comment to those channels, not here. Plus, integrals Dr PK do are all different ones. Not make them slightly different. You are saying that because you are not good at integrals and dont know much of it.
@ Be real. You hate integrals or math olympiad because you are bad at math. Real analysis or topology? if you wanna learn, go learn and stop whining here. No one wants whining from people like you
I guess it is mostly you. I enjoy integrals and also competition maths so much. Integrals and olympiad math questions are the choice from math youtubers. You do not have a right to blame them just because you do not enjoy them. If you like abstract algebra, or real analysis, you just find those channels, and watch the videos. But, once again, you do not have a right to blame anyone