Sequences were learned in IM1, specifically the arithmetic and geometric types. Since then, we have discovered patterns regarding quadratic and cubic relationships using higher order constant differences, and through enough intuition we can work out most any special case we put our mind to. This section poses that challenge for us in the 61-problem set, plus having subtle implications that you remember all about arithmetic and geometric sequences along the way.
We are also introduced to series (plural for "series," heh!), which is the sum of the list of terms in a sequence regardless of its type. The reason for summing the list might become instantly justifiable in what kinds of questions are asked in the word problem set, but with it comes a slew of new formulas for which we have yet to even scratch the surface. Want to find the sum of the first n positive integers? We have a formula for that. We also have it for the squares of the first n positive integers as well. In future sections, we'll be able to find the sum of any arithmetic or geometric series using other formulas.
Sigma notation (aka "summation notation") is the last new item covered, which uses the Greek letter Sigma (Σ) as a function to generate the series for a string of numbers given a rule and input bounds. These are ones that will simply take a moment of time to absorb, daunting as they appear. Sometimes we have to write out the Sigma notation, and other times we have to evaluate the sum.
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*PDF DOWNLOADS*
Textbook (7.1): https://smallpdf.com/file#s=3ac1a896-3b94-42d2-9af7-6c255dd991e5
Graph paper (scaled): https://docdro.id/flV4fYe
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*TIMESTAMPS (separated by section)*
(0:00:00) Introduction
(0:01:02) Lecture overview
(0:21:39) Problem #1-4
(0:24:08) Problem #5-14
(0:33:10) Problem #15-26
(0:56:36) Problem #27-28
(1:00:14) Problem #29-30
(1:08:13) Problem #31-38
(1:20:18) Problem #39-50
(1:07:23) Problem #33-34
(1:14:36) Problem #35-36
(1:20:03) Problem #37-44
(1:29:55) Problem #45-46
(1:36:24) Problem #47-50
(1:37:16) Problem #51-52
(1:41:23) Problem #53
(1:47:26) Problem #54-55
(1:53:31) Problem #56
(1:56:53) Problem #57
(1:58:19) Problem #58
(2:01:26) Problem #59
(2:09:13) Problem #60
(2:11:44) Problem #61
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*BIG IDEAS MATH (IM3) PLAYLIST*
https://www.youtube.com/playlist?list=PLsWOyuFufO779Te_I5J78GCU60qekMG-Z