# Writing arithmetic series in summation notation

In this expression c is a constant, i.

### Sigma notation rules

The variable of summation, i. It looks like we're adding two every time so it looks like this is an arithmetic series. Two times is plus seven is indeed Arithmetic operations may be performed on expressions containing more than one variable. 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. Summation notation involves: The summation sign This appears as the symbol, S, which is the Greek upper case letter, S. The summation sign, S, instructs us to sum the elements of a sequence. And so how many total terms are we going to have here? So is seven plus two times what? Well, one way to think about is I just shifted the indices up by one so we're going to go from k equals one to So we're at seven and then we're going to nine and then we're going to So let's think about this a little bit. When k equals zero, this is just going to be seven. Notice, the first term works out because we're not adding two at all so one minus one is equal to zero so you're just going to get seven.

So this is going be a sum, a sum from, so there's a couple of ways we could think about it. Another way, we could also write it as, let me do this in a different color, we could, if we want to start our index at k is equal to one then let's see, it's going to be the first term is going to be seven plus two times k minus one, times k minus one.

Then when k is equal to two, the second term, we're going to add two one time because two minus one is two so that gives us that one.

## How to write sigma notation

We have seven plus nine plus 11 and we keep on adding all the way up to In this expression c is a constant, i. Another way, we could also write it as, let me do this in a different color, we could, if we want to start our index at k is equal to one then let's see, it's going to be the first term is going to be seven plus two times k minus one, times k minus one. Infinite geometric series Video transcript - [Voiceover] What I want to do in this video is get some practice writing series in sigma notation and I have a series in front of us right over here. So either way, these are legitimate ways of expressing this arithmetic series in using sigma notation. So that's one way that we could write it. 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. 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. Then the notation below and above the summation sign is omitted. Therefore this expression means sum the values of x, starting at x1 and ending with xn. For example: This expression means sum the values of x, starting at x1 and ending with xn and then square the sum. This is going to be, we could write it as seven plus two times k. Arithmetic operations may be performed on expressions containing more than one variable. Summation notation involves: The summation sign This appears as the symbol, S, which is the Greek upper case letter, S.

Therefore this expression means sum the values of x, starting at x1 and ending with xn. Summation notation involves: The summation sign This appears as the symbol, S, which is the Greek upper case letter, S. So is seven plus two times what?

A typical element of the sequence which is being summed appears to the right of the summation sign. Arithmetic operations may be performed on expressions containing more than one variable. When k is equal tothis is going to be minus one which is Let x1, x2, x3, …xn denote a set of n numbers.