# Writing a sum in summation notation

### Use summation notation to write the sum

But instead, what I like to do, is look at our options. This is n is equal to one. Arithmetic operations may be performed on variables within the summation. Which expression is equal to the sum above? And we stopped at n equals four 'cause it tells us right over there, we start at n equals one and we go all of the way to n equals four. And then plus, finally, 'cause we stop right over here at n equals four, when n equals four, it's going to be k over four plus one. That's n is equal to three. Well, only this one is starting with a k over two. Let me write it down. You're adding three each time. Let's do the situation when n is equal to one. That is five. A typical element of the sequence which is being summed appears to the right of the summation sign. This is what we got when n equals two.

So plus three times, when n equals four, this is three times four minus one. That is five.

We start at two, when n equals zero, this is just, that three n is just zero. The summation sign, S, instructs us to sum the elements of a sequence.

Now we could try to construct an equation here or an expression using sigma notation. So at n equals two, two plus three times two is two plus six, which is eight.

## Rewrite each series using sigma notation

Now let's do the same thing over here. So that's what they're trying to do here. So like always, pause the video, and see if you can work through this on your own. Arithmetic operations may be performed on expressions containing more than one variable. What sum would each of these be? So this is going to be three times, when n equals one, three times one minus one. This is n is equal to one. The index assumes values starting with the value on the right hand side of the equation and ending with the value above the summation sign. Once again, still looking good. Let's do the situation when n is equal to one. And so this also is exactly the same sum. Therefore this expression means sum the values of x, starting at x1 and ending with xn. Well, like we did before, let's just expand it out. So plus three times, when n equals four, this is three times four minus one. That's n is equal to three.

When n is equal to one, it's gonna be k over one plus one. We really only have to look at these two options here and expand them out. So like always, pause the video, and see if you can work through this on your own.

## Summation notation calculator

So what does this equal? Three times two minus one. Let's do one more example. That's when n is equal to four. Other common possibilities for representation of the index are j and t. So when you look at the sum, it's clear you're starting at two. Well, only this one is starting with a k over two. When n is equal to zero, it's going to be two plus three times zero. Summation Notation Often mathematical formulae require the addition of many variables Summation or sigma notation is a convenient and simple form of shorthand used to give a concise expression for a sum of the values of a variable. Once again, still looking good. We start at two, when n equals zero, this is just, that three n is just zero. N equals one.

But instead, what I like to do, is look at our options. So we definitely feel good about choice A. N equals one. And what's different here is that we just have a variable, but that shouldn't make it too much more difficult.

So we're here, we're given the sum, and we're saying choose one answer.

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