![]() ![]() Just be able to pick it out by inspecting this here, butįor the sake of this example, let's expand this out a little bit. ![]() So what is our first termĪnd what is our common ratio? And what is our n? Well, some of you might So let's apply that to thisįinite geometric series right over here. The sum of the first n terms is equal to our first term times one minus our common ratio to the nth power all over Ourselves in a previous video we derived the formula where Let's do some examples where we're finding sums If you review the video "Geometric series intro" (the first in this sequence), at around I don't know where he uses the phrase you mention (defining n as the "upper limit" of a sum), but the expression sounds ambiguous to me, or even misleading (I didn't see it in the previous video, "Geometric series with sigma notation." If you know where Sal used it, I would be interested in getting the reference to it: video name and time-stamp). ![]() This distinction between k and n can be confusing, and Sal didn't make the distinction clear in this sequence of videos. If you are interested in more explanation, here's a start (but you can skip it if it just makes things more confusing !-) : A slight change in the formula you give would make it correct in the example Sal is using here: just substitute k for n (in the formula you give), and you will come up with the same values that Sal finds. It's this value that we use in the formula for the series. 99 is the maximum value of k, but since k begins with the value 0, there are k+1 terms, or 100. The letter n (which is used here in the formula defining the value of a sum) is the number of terms in the sequence/sum, not the maximum value of k (which is the index used in the sigma formula). ![]()
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