Online Course Discussion Forum

 
 
Picture of shawn luo
by shawn luo - Thursday, 6 February 2020, 6:11 PM
 

what does  ∑ mean?

 
Picture of Areteem Professor
Re: ∑
by Areteem Professor - Friday, 7 February 2020, 10:58 AM
 

$\Sigma$ is the Greek letter Sigma. In math we use it to express large sums in a short way. Under the $\sum$ symbol we write which variable we will be using and its starting value; on the top we write the largest value of the variable to be used; then we sum all of the values obtained by plugging in the variable in the formula to the right of $\sum$.

For example $$1 + 2 + 3 + 4 + 5 + \cdots + 1000 = \sum_{k = 1}^{1000} k,$$ $$1 + 3 + 5 + 7 + \cdots + 999 = \sum_{k =1}^{500} 2k - 1,$$ or $$1^2 + 2^2 + 3^2 + \cdots + 100^2 = \sum_{k=1}^{100} k^2.$$

Under the $\sum$ symbol it tells us that we will be adding the values we get by plugging in values of $k$ starting from $1$ and up to the value at the top of $\sum$.