00:01
All right, so we have summation i to some arbitrary number n with expression with terms 7j plus 4 over n squared.
00:26
And we're going to represent that with e is going to be the sigma form.
00:37
1 is less than equal i less than i less than equal to n and then 7j plus 4 divided by n squared and we don't have any formula for a division of n squared but we because every term is being divided by n squared we can just take this out and divide the entire summation by n squared so we get 1.
01:09
Over n squared times e just get and so we don't have we also don't we can't do both terms right at once we want to separate this into two summation so we get all of this and then this is going to be one term with just the j.
01:55
Oh, we're just going to be j, and j, and then we're going to add another summation with just the con, but this time with just the constant four.
02:22
And so again, we don't have, we can't, since we're going to be times in this summation, since we're going to be timing j by seven every single time, we can just take it out and times the entire summation by seven.
02:40
So we'll just take this out.
02:42
We get 7 times e and so on.
02:48
And in section 4 .2, we have the formulas for summation of j is just going to be n, n plus 1 over 2.
03:00
And for some constant c, which is going to be 4, it's going to be c times n.
03:06
So we get 1 over n squared times times.
03:17
Times 7 times n plus plus 1 over 2 for this for this summation and this is going to be c times n c is going to be 4 here so if we want to put this all in so if we want to simplify this term, all this, we're going to get 7 times n squared here times 7 because 7 times n squared plus 7 times n.
04:50
And then if we want to do this again, if we want to simplify it further, we're going to have this be 8 over 2.
05:10
And then we can bring this, and then we can times all this by 1 over n squared here.
05:17
And we can bring this into all of.
05:20
And then this is going to give us 8.
05:31
We can add 7n and 8 n...