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And then our fourth term, our fourth term is negative three.

I'm just really copying this down, but I'm making sure we associate it with the right term.

- [Narrator] Nth partial sum of the series, we're going from one to infinity, summing it a sub n is given by.

And they tell us of the formula for some of the first n terms.

So if I have a sub one plus, plus a sub two, plus a sub three, and I keep adding all the way to a sub n minus one plus a sub n.

This whole thing, this whole thing that I just wrote out. This whole thing is s, let me this whole thing is sub n, which is equal to n plus one, over n plus 10.

So we have n times n plus 10, over n plus nine times n plus 10. And then this right over here this is n squared plus 10 n, within that red color.

So this is n squared plus 10 n and remember we're gonna subtract this.

Well wherever we see an n, we'd replace with an n minus one. So it's equal to six times three six times three. A sub four is going to be equal to A sub three, A sub three times A sub two. So times A sub two, times A, and then a blue color. And then finally A sub four, which I will do in a color that I'll use, I'll do it in yellow.And this is actually going to be the case for n greater than one.For n equals one, s sub one is going to be, well you can just, a sub one is going to be equal to s sub one.

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