Sequences, Factorials, and Summation Notation

[@farhanahmed2508]

*He knows about all kinds of stuff... Professor Dave Explains!* Love it.

[@science-y9209]

Well it's "he know A LOT about all kinds of stuff..."

[@bobby9108]

You forgot the "woom" at the end

[@charliechuma8061]

Yah,but it doesn't mean shit if he can't explain it

[@farhanahmed2508]

@@charliechuma8061 He's got a whole channel explaining it

[@Tusharplays69]

​@@farhanahmed2508i like how you replied to a reply that's been done almost 5 years after you commented.

[@ConceptualCalculus]

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.

[@connorconnor2421]

For factorials, the sequence rule is: a(n) = n * a(n - 1).

[@josefkay5013]

As long as you define a(0) := 1

[@MiltosPol-qn3zh]

I was waiting for this video a lot of time. I finally understood what does this sigma means.

[@SteelBB9]

ITS ME I AM THE SIGMA

[@saketpanigrahi]

9:32 we can add and find sum =-1/12

[@teamSwaleOfficial]

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.♥️

[@trhll5635]

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

[@thatsnotme3235]

Would you mind adding this to the calculus playlist??? I was wondering why I hadn't watched this before!

[@ProfessorDaveExplains]

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!

[@ivoryas1696]

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...

[@RedRahiq]

2:41 Isn't each term the double plus one of the previous ? Or that there is no sequence with that type ?

[@olivernardbagay318]

well explained! helped me a lot!

[@memeingthroughenglish7221]

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.

[@ivoryas1696]

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.

[@AllYourMemeAreBelongToUs]

This is actually really good.

[@yuqingcai3447]

Thank you, sir! You are literally saving my life

[@MiltosPol-qn3zh]

One question. What does i=1(for example) under sigma means???

[@ProfessorDaveExplains]

it means start the summation at i = 1, so you start by plugging in 1 and go from there!

[@MiltosPol-qn3zh]

Professor Dave Explains Thanks,professor!!!!! Are you going to make a tutorial about capital pi???

[@OnursDressT]

this is a very good introduction to analysis at uni

[@Pegisus2501]

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! 🥰🎉👍🏽💻

[@ivoryas1696]

Pegisus2501 "I'm not longer scared of math" A blessed sentence if _I've_ seen one!

[@sweatydood5118]

Could you do some multivariable calculus?

[@ProfessorDaveExplains]

don't worry i'll get there!

[@jamesb9567]

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.

[@Kammerliteratur]

yes, i had exactly the same problem. i figured that the numder, by wich the sequence icreases, increases by 4 each time.

[@zahriddinbahodirov9520]

I love your lessons, thank you, inshallah I'll soon learn physics course too

[@Nemoguzapomnit]

Thx for that video. How you see the patterns for series?

[@allynreign433]

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?

[@LloydSMITH]

Very simple Actually ! : )

[@primalpiano7580]

Lloyd Smith you have the Coolest channel ever !

[@vedansh7010]

Professor Dave for the first comprehension question can the answer be :: an-1 +3?

[@GodbornNoven]

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!

[@lucas5262-h1y]

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.

[@kai.acadventure]

Could you explain whether 0 considers an even number? it makes me confused at 1:05

[@science-y9209]

Something is definitely missing..cuz i didn't get it at all.. unlike your previous videos..even the ones on calculus

[@_Ten_]

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?

[@Name-is2bp]

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...

[@chadani4768]

Yes

[@HussamJihaz]

Nice vid as always!

[@designingworld6611]

no, it's the worst video ever

[@Rokanlevio]

when i have the sigam notation i always use i in stead of n is this a problem ?

[@highflierpriyanka]

Great video!

[@joshuanuguse8795]

thanks very much

[@arinzeanthony7447]

My problem is how to write those rational ones in closed form.

[@HelloHeloWorld]

This was so fun to solve.

[@mostafamandour5278]

I got this for second example (n+n)×n 🙂 .., try to plug the number and you will get the exact answer , easy enough 😅

[@unknownbeing8222]

How do we determine the lower limit?

[@koamivikeledome]

Thanks

[@n.v.n.prasad132]

What is the capitalised pi notation? I heard it’s used for summation as well

[@Vagabond-Cosmique]

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)

[@n.v.n.prasad132]

@@Vagabond-Cosmique thank you!

[@Soupy_loopy]

This reminds me of the time when I had a good comment

[@RadoHudran]

6:09 How do you know what a1, a2, ... is equal to if it wasn't specified?

[@RadoHudran]

Nobody said a(n)=n

[@DefinitelyNotFelis.]

Yeah, it was the only thing I didn't quite understand from this lesson.

[@philmaguire4042]

Straight away I’m lost. What is a sub n?

[@ProfessorDaveExplains]

the little n in subscript

[@UziMan-Science-Math]

Can e be expressed like this? ∞ Σ (1/n!) n=1

[@serbrad6426]

my humble respect to Sir Isaac Newton

[@tGoldenPhoenix]

Done.

[@AyisatLawalShittu]

I got no comprehension questions right

[@tyranttitanium5721]

Came for the flat earth videos, stayed for this.

[@enriquesalazar2538]

I got lost after sequence

[@sad_man_no_talent]

he knows stuff but not a lot of stuff

[@diganta7]

why the heck does he looks like shakes pear!?

[@priencessme6100]

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

[@science-y9209]

Please brush up your english

[@RedRahiq]

Then don't come here. What's ur problem?

[@nameisfarabi4596]

Ughhhhhhhhhhhhhhhhhhhhhhhhhhhhh

[@hastylegend1365]

feed me more🤩🤩🤩🤩🤩

[@janedoes5903]

He didn't explain well. Didn't explain much at all just stated facts.

[@ProfessorDaveExplains]

No, I also explained it quite thoroughly. The channel is called Professor Dave Explains. Watch it one more time.

[@udayseul1535]

He might be blind. Or dump