Sequences, Factorials, and Summation Notation

You may have this scary looking upper case sigma before. But don't worry, it just means to add some things up! Once we understand how series work, we can do all kinds of other things. Also, have you ever seen numbers with exclamation points after them? No it, doesn't mean that you shout the number. Those are factorials! We will learn about those in here as well. Lots of good stuff in here!

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[farhanahmed]

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

[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.

[connorconnor]

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

[MiltosPol-qnzh]

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

[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.♥️

[thatsnotme]

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

[memeingthroughenglish]

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.

[Pegisus]

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! 🥰🎉👍🏽💻

[yuqingcai]

Thank you, sir! You are literally saving my life

[MiltosPol-qnzh]

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

[zahriddinbahodirov]

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

[allynreign]

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?

[kai.acadventure]

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

[vedansh]

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

[Nemoguzapomnit]

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

[_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?

[lucas-hy]

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.

[mostafamandour]

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

[ivoryas]

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...

[OnursDressT]

this is a very good introduction to analysis at uni