Your comprehension check at the end uses the word "series," but what you have there are sequences. A sequence is a list. A series results from adding the numbers in the list together.
9:31 mathematician ramanujan from India gave the theorem regarding the sum of all the natural numbers upto infinity and that was. -1/12 it can be confusing that how can the sum of natural numbers be a negative fraction but this is the magic of srinivasan Ramanujan. Please don't say after today that numbers till ♾️ can't be added. And thank you for such an amazing video.♥️
Srinivasa Ramanujan’s answer is -1/12, because his summation method isn’t both linear and stable, and so what’s most likely intended by Dave is that if you tried to use a linear and stable summation method towards the series 1 + 2 + 3 …, then you will not have any finite solution, and this makes sense in the context of Professor Dave’s mathematics tutorials, as he hasn’t taught anything before this video about non-linear and unstable summation methods
well the introduction to these concepts is taught in algebra, so in the math playlist this happens way before calculus, i figured just linking to it with a card would be enough!
Might I mention how *truthfully **_based_* it is that Dave teaches sequences so early? I didn't these things in college and they feel _largely_ out of place in their conceptual simply being introduced *_after_* limits...
Your explanation of e was really cool! Can you make a really in-depth video about e? I feel like it's everywhere, but still kind of mystifying. The same with ln.
memeingtheoughenglish7221 Tbh, yeah. I saw it in, like, _one_ class in highschool. For such an incredible number as it's often touted, doesn't seem to receive proper treatment until softmore undergrad. Like James Maxwell.
hii, i would like to ask if i can find the sigma notation ‘E’ with using only the series, if that makes sense. for example. (2,4,6,8,10) i have to find the ‘E’ of this series. is there a formula to find a sigma notation with using only the series?
Totally Awesome Prof. Dave. 🥳 You've made it so easy to understand. 🤩 I'm no longer scared of math! 🥳 The college textbooks don't even compare to what you give us here. 😊 I can finally see myself understanding computer graphics! 🤩 Thank you so much! 🥰🎉👍🏽💻
After some brain mashing, my answer to the second question was "a(n) = (a(n-1) - a(n-2)) + a(n-1) + 4". Seeing the actual answer made me cringe(at myself). Anyways, thanks prof.
Sir😂😂😂😂 I can't understand do u all tym make just videos.u know I...think that when tym come I will study this stuff now I HV to see first my maths syllabus maybe so I really not interested in ur vid sorry to say
*He knows about all kinds of stuff... Professor Dave Explains!* Love it.
Well it's "he know A LOT about all kinds of stuff..."
You forgot the "woom" at the end
Yah,but it doesn't mean shit if he can't explain it
@@charliechuma8061 He's got a whole channel explaining it
@@farhanahmed2508i like how you replied to a reply that's been done almost 5 years after you commented.
Your comprehension check at the end uses the word "series," but what you have there are sequences. A sequence is a list. A series results from adding the numbers in the list together.
For factorials, the sequence rule is:
a(n) = n * a(n - 1).
As long as you define a(0) := 1
I was waiting for this video a lot of time. I finally understood what does this sigma means.
ITS ME I AM THE SIGMA
9:32 we can add and find sum =-1/12
9:31 mathematician ramanujan from India gave the theorem regarding the sum of all the natural numbers upto infinity and that was. -1/12 it can be confusing that how can the sum of natural numbers be a negative fraction but this is the magic of srinivasan Ramanujan. Please don't say after today that numbers till ♾️ can't be added. And thank you for such an amazing video.♥️
Srinivasa Ramanujan’s answer is -1/12, because his summation method isn’t both linear and stable, and so what’s most likely intended by Dave is that if you tried to use a linear and stable summation method towards the series 1 + 2 + 3 …, then you will not have any finite solution, and this makes sense in the context of Professor Dave’s mathematics tutorials, as he hasn’t taught anything before this video about non-linear and unstable summation methods
2:41 Isn't each term the double plus one of the previous ? Or that there is no sequence with that type ?
Would you mind adding this to the calculus playlist??? I was wondering why I hadn't watched this before!
well the introduction to these concepts is taught in algebra, so in the math playlist this happens way before calculus, i figured just linking to it with a card would be enough!
Might I mention how *truthfully **_based_* it is that Dave teaches sequences so early? I didn't these things in college and they feel _largely_ out of place in their conceptual simply being introduced *_after_* limits...
well explained! helped me a lot!
Could you explain whether 0 considers an even number? it makes me confused at 1:05
One question. What does i=1(for example) under sigma means???
it means start the summation at i = 1, so you start by plugging in 1 and go from there!
Professor Dave Explains Thanks,professor!!!!! Are you going to make a tutorial about capital pi???
Thank you, sir! You are literally saving my life
This is actually really good.
Thanks for the video. I'm a little confused at 2:20 . How does 2 * 3 to the N power - 1 give us 18 or 54?. Is N the term number?
2 * 3 ^ (1 - 1) = 2 * 3 ^ (0) = 2 * 1 = 2
2 * 3 ^ (2 - 1) = 2 * 3 ^ (1) = 2 * 3 = 6
2 * 3 ^ (3 - 1) = 2 * 3 ^ (2) = 2 * 9 = 18
2 * 3 ^ (4 - 1) = 2 * 3 ^ (3) = 2 * 27 = 54
....and so on...
Yes
Your explanation of e was really cool! Can you make a really in-depth video about e? I feel like it's everywhere, but still kind of mystifying. The same with ln.
memeingtheoughenglish7221
Tbh, yeah.
I saw it in, like, _one_ class in highschool.
For such an incredible number as it's often touted, doesn't seem to receive proper treatment until softmore undergrad.
Like James Maxwell.
this is a very good introduction to analysis at uni
Thx for that video. How you see the patterns for series?
hii, i would like to ask if i can find the sigma notation ‘E’ with using only the series, if that makes sense. for example. (2,4,6,8,10) i have to find the ‘E’ of this series. is there a formula to find a sigma notation with using only the series?
Totally Awesome Prof. Dave. 🥳 You've made it so easy to understand. 🤩 I'm no longer scared of math! 🥳 The college textbooks don't even compare to what you give us here. 😊 I can finally see myself understanding computer graphics! 🤩 Thank you so much! 🥰🎉👍🏽💻
Pegisus2501
"I'm not longer scared of math"
A blessed sentence if _I've_ seen one!
6:09 How do you know what a1, a2, ... is equal to if it wasn't specified?
Nobody said a(n)=n
Yeah, it was the only thing I didn't quite understand from this lesson.
Could you do some multivariable calculus?
don't worry i'll get there!
I love your lessons, thank you, inshallah I'll soon learn physics course too
So I got a different answer for 1) a1 + 3(n-1) = an
Would that be wrong? It still works but I think I over complicated it.
when i have the sigam notation i always use i in stead of n is this a problem ?
Professor Dave for the first comprehension question can the answer be :: an-1 +3?
Very simple Actually ! : )
Lloyd Smith you have the Coolest channel ever !
After some brain mashing, my answer to the second question was "a(n) = (a(n-1) - a(n-2)) + a(n-1) + 4". Seeing the actual answer made me cringe(at myself). Anyways, thanks prof.
yes, i had exactly the same problem. i figured that the numder, by wich the sequence icreases, increases by 4 each time.
What is the capitalised pi notation? I heard it’s used for summation as well
Capital sigma is for summation, capital pi is for product.
So Π(n) = n×n×n×n×n×n...
en.wikipedia.org/wiki/Product_(mathematics)
@@Vagabond-Cosmique thank you!
Great video!
Nice vid as always!
no, it's the worst video ever
How do we determine the lower limit?
This was so fun to solve.
thanks very much
My problem is how to write those rational ones in closed form.
I got this for second example (n+n)×n 🙂 .., try to plug the number and you will get the exact answer , easy enough 😅
Thanks
Something is definitely missing..cuz i didn't get it at all.. unlike your previous videos..even the ones on calculus
This reminds me of the time when I had a good comment
Straight away I’m lost. What is a sub n?
the little n in subscript
Can e be expressed like this?
∞
Σ (1/n!)
n=1
Came for the flat earth videos, stayed for this.
Done.
my humble respect to Sir Isaac Newton
I got no comprehension questions right
he knows stuff but not a lot of stuff
I got lost after sequence
n + 3
???
n.n! + n
why the heck does he looks like shakes pear!?
feed me more🤩🤩🤩🤩🤩
Sir😂😂😂😂 I can't understand do u all tym make just videos.u know I...think that when tym come I will study this stuff now I HV to see first my maths syllabus maybe so I really not interested in ur vid sorry to say
Please brush up your english
Then don't come here. What's ur problem?
Ughhhhhhhhhhhhhhhhhhhhhhhhhhhhh
He didn't explain well. Didn't explain much at all just stated facts.
No, I also explained it quite thoroughly. The channel is called Professor Dave Explains. Watch it one more time.
He might be blind. Or dump
2+3(0)2+3(1), 2+3(2)
n=0
2+3n
2,8,18,32
Let's divide by 2
1,4,9,16,25
2n² as n=1 until n
1,2,6,24,120
n!