00:02
Now let's look an example where they give us an expanded expression, and they would like us to write it as the summation notation that would expand out to be that expression.
00:13
So here i have in the bracket 7 times 1 6 plus 5, then close the bracket, plus 7 times 2 6 plus 5, close the bracket, et cetera.
00:24
And notice from term to term from what's in the brackets from one to the other, what is the same in each thing.
00:32
Because that will be a constant and not be incremented up with your index of summation.
00:37
So in each of these, i have a seven, multiplied to a fraction where the denominator is six, but the top is incrementing.
00:47
So i have a seven that's consistent in every term, then times that's consistent.
00:53
The denominator of six is the same in each one, and then plus the five is the same in each one.
01:00
The only thing that's changing is the numerator of the fraction.
01:04
It's going first with a one, then a two, then a three, all the way up to then a six.
01:09
So that part that's fixed will be those numbers, and that part that's incrementing up will actually have our index of summation and then show what they're supposed to start with and end with that.
01:22
So we have our summation, and that's representing the pluses between these grouping.
01:31
And i can pick whichever index of summation i want for the letter part.
01:36
I could do i or k or j or whatever...