Introduction to Sequences (Precalculus - College Algebra 67)

[@user-bh6jk3yk7v]

damn, imagine how hard our lives would've been if professor Leonard didn't get up one day and said to himself "Hey I am going to upload my classes to youtube"

[@ProfessorLeonard]

Note: While '0' itself IS an even number (and can be defined so), it depends on how we denote the sequence as to whether it is the 'first' even or not. We can say that 2 is the first POSITIVE even number without ambiguity. But in defining the sequence as beginning with n=1, we are avoiding the even term of zero. I make an allusion to this a bit earlier in a different example when I state that zero acts as an even number for the exponent of -1 even though the terms are not beginning with n=0 but n=1 and so for our sequences, zero is not part of the even 'list' but for exponents it absolutely acts as even (because it is) which was the meaning of the statement I made. And so, zero is excluded from the list of even numbers simply because of the way we define them with a sequence in starting with n=1. If we begin with n=0, then we actually have the first even number of '0' and get 51 even numbers when we reach the n=50 term. I tried to keep the video brief, and so did not want to delve into this on film, but it's a great question and I hope my writing makes sense.

[@johnwarner8641]

professor Leonard, i want to thank you for your great lectures.

[@anasqureshi4606]

Ive cleared my exams 2 years before,I used to listen to you every day,but now I'm missing you,since I have no reason to study

[@WOLF91]

I love the way this man teaches. Thank you so much.

[@georgesadler7830]

Professor Leonard, thank you for an exceptional video/lecture on the Introduction to Sequences. This material is very helpful for students taking Calculus Two. The whole idea of this topic is pattern recognition from start to finish.

[@kowkingder8389]

Best teacher of all time

[@jay22197]

this guys is so much better than my professor

[@mattychase]

We all can’t thank you enough. ❤

[@phenol6783]

Pog Prof letting us all have this for free! Many thanks!

[@eobardrush2112]

I have been waiting for this!!

[@nihatdonmezov8354]

At 38:59, the exponent of (n+1) also works.

[@PhillipRhodes]

You could also just use n as the exponent and put a negative sign in front of the entire expression. In R code: series_func

[@dr3d3smondAd3sina]

n+1 will not work sir. at n = 4 then what do you get? the series will (-1) raise to 5 * 2 that is 10 not 8 and at n = 6 you get 12 not 10

[@Monestfiks]

@@dr3d3smondAd3sina he says take the exponent not the 2 n

[@rosy6756]

Love you Leonard ❤️❤️💖💖

[@chahinezbouteldja7473]

Professor Leonard I wish if I had a teacher like u in analyse math ❣❣🙏🙏

[@muntoo1]

Prof Leonard, can you be so kind to do another video explaining the index k and n in the summation of sequences?

[@busrraengin]

Thank you, Professor!

[@danielbrillantes2791]

Thank you sir.

[@usv-ju6lg]

What about : bn=n+(n-1) it seems working perfectly. you don't need to know any previous item , try it for b100 and b99

[@jodielprynce]

Such a very informative lecture!

[@Wahab7168]

The recursive function of the last question wouldn’t work right? Try it on b sub 1, you get 2 out of b sub 0, so it wouldn’t work

[@zuxzux]

For the sequence at 38 min, you could also use n+1 as the exponent correct? That should give you the same result.

[@marlenarteaga2154]

Would you consider doing videos for actuary students?

[@thatsounditmakes9177]

At 37:53 for b_1 I'm getting -1^0 = -1 so the result b_1 = -2 not b_1 = 2, even though I got the same final expression. What am I doing wrong?

[@aareview8258]

-1^0 is 1

[@fredtanada3388]

Check your order of operations. Recall PEMDAS. So when you plug in -1^0 in your calculator, the exponent gets evaluated that first, then you multiply. So in this case, the calculator evaluates 1^0 first which gets us 1. Then, it multiples by -1 to get -1. If you want to get a result of 1, you have to plug it in like this (-1)^0 in your calculator because of PEMDAS.

[@MrOsha7]

for the sequence in min 50:00 cant I write it as n+(n-1) as well and that would work just as fine?

[@dragmahk]

You can remove the parenthesis n+n-1 and combine like-terms and you end with 2n-1 which is the video formula

[@algoexplanations4418]

Hi Do you have problems and homework solutions alongside this class? I would be willing to pay for such a course

[@ugddgg9461]

Sir you are the best for sure sir when you complete this chapter can you make a video in topic average mean value in which we use integration and find that and a RMS value sir please make it ❤️❤️❤️

[@williammendez5209]

That's too specific.

[@eobardrush2112]

Yeah thats too specific Ease down buddy you can find those on other parts on the Internet