00:01
So we have this series, 3 and then minus 9 plus 27, minus 81, plus 243, minus 729.
00:13
And we want to write it in sigma notation.
00:15
So we know we want the sum of, let's say i go i equals 1, 2, and we have 1, 2, 3, 4, 5, 6 terms.
00:23
So we have 6 terms.
00:23
So we know we're summing up 6 things.
00:26
And i can see that this is geometric.
00:29
I keep multiplying by negative 3, or the common ratio between consecutive terms is negative 3.
00:39
Let's see, negative 3 times negative 3.
00:42
Okay, so i'm going to write it as the first term times the common ratio, and the common ratio is negative 3, to the, and i'm going to go i -1 power.
00:58
And we've got our rule.
00:59
So we always have the first term, the common ratio, to the n -1 -1 -1, or in our case, the i -minus -1 power...