00:01
So in this problem, we want to represent each sum using summation notation, meaning we need to use our sigma simple.
00:06
So the first thing we're going to do is write a formula to help us find any term in this formula.
00:12
So let's look at our basis here.
00:13
We start at negative 2, negative 1, et cetera.
00:16
So notice we're increasing by 1.
00:18
But we're not starting at 1.
00:20
So we have to think of what number when we were substituted in 1 for n, we subtract what, i'm going to call it x, to get negative 2.
00:28
Well, if i subtract 1 from both sides, negative x would be negative 3, so x would be 3.
00:33
So to get each of these terms from the term in the sequence they are, we take away 3 from it, which means that if we take n and subtract 3 from it, that will give us our base.
00:43
And then notice our exponent for each of these is 5.
00:46
So now we have our formula to find any term.
00:49
Now, in terms of what we're going to put with our sigma symbol, at the bottom, remember, we started when n was equal to 1, so we'll put that on the bottom, then how many terms are there? well, if you think about it, from 1 to 7 would be 7, include 0, negative 1, and negative 2, so to be 10 terms.
01:04
So, we have 10 in the top.
01:05
So now we have the answer to part a.
01:08
Next, let's take a look at part b.
01:10
So in part b, we have negative 2 plus negative 1, plus 0, plus 1, plus 2, plus 3, plus 4, plus 5.
01:22
Okay, so again, we're going to write this by using significant notation.
01:26
So again, first off, we need our formula.
01:28
We'll notice our first term is negative 2 again for our base, and we continuously add 1.
01:33
So it's going to be the same formula.
01:34
It's going to be n -33.
01:36
All right, so then underneath our sigma symbol, we're going to do n equals 1, and how many terms are there? there's 1, 2, 3, 4, 5, 6, 7, 8...