Introduction to Sequences (Precalculus - College Algebra 67)

Comments · 43

• US

  @user-bh6jk3yk7v · 5 years ago

  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"

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• PR

  @ProfessorLeonard · 5 years ago

  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.

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• AN

  @anasqureshi4606 · 5 years ago

  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

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• WO

  @WOLF91 · 5 years ago

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

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• JA

  @jay22197 · 5 years ago

  this guys is so much better than my professor

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• MU

  @MufkyVT · 9 months ago

  It&apos;s really eye opening to see the step of breaking down the outputs into ones that are similar to one another and then relate the changing numbers to the index.<br><br>Deeply appreciate you teaching this important aspect when other videos just tell you to identify a ratio and memorize a formula which is not enough and had me confused for awhile.

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• GE

  @georgesadler7830 · 4 years ago

  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.

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• RO

  @rosy6756 · 5 years ago

  Love you Leonard ❤️❤️💖💖

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• CH

  @chahinezbouteldja7473 · 5 years ago

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

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• MA

  @mattychase · 3 years ago

  We all can’t thank you enough. ❤

• AN

  @animecliphub-f · 4 months ago

  math during the day and fighting crime at night. i used to think the glasses werent a good disguise but i guess they are

• KO

  @kowkingder8389 · 3 years ago

  Best teacher of all time