00:01
We have the infinite series 1 minus 3 fourths plus 9 .16s minus and so on forever.
00:09
Does this converge or diverge? in order to determine this, we need to look at r, the common ratio.
00:15
There's a statement in the book saying that if the absolute value of the common ratio is less than one, then we'll have a convergent series.
00:23
So let's find r.
00:25
Well, to find r, we just have to divide one term by the previous, such as negative three quarters by one.
00:32
It doesn't matter which two terms we pick as long as they're consecutive.
00:35
That's what's so useful about r.
00:37
It doesn't matter which two terms you use.
00:39
And this comes out to, of course, negative three -fourths...