Notation to use for operation Lets say I have some numbers: 
[1, 3, 5, 1, 10, 8]
What is the proper mathematical notation for the following operation?
$$ (1-3) + (3-5) + (5-1) + (1-10) + (10-8) $$
Here is what I was trying:
$$ \sum_{i=1}^{N} p_i - p_j$$
Is this correct? If now, what is the best way to write this?
 A: If there are $N$ numbers in the sequence, and we call the $i$th number $p_i$, then your operation just gives $p_1-p_N$.
A: Your $p_j$ doesn't make sense because you don't have $j$ anywhere else.  But you're close.  Suppose your numbers are $p_1, p_2, \ldots, p_N$.  Then the expression you want is
$$\sum_{i=1}^{N-1} p_{i} - p_{i+1} $$
Here if $p_i$ is one of the numbers in the sequence, then $p_{i+1}$ is the next number.  So it says that from each number $p_i$, we subtract the next number $p_{i+1}$, and then the $\sum$ says to add up all the differences.
Note that we add only up to $i=N-1$, since after that there is no next number to subtract from: when $i=N-1$, the $p_{i}-p_{i+1}$ expression becomes $p_{N-1} - p_{N}$, and we are subtracting the ḷast number from the next-to-last  one.
As Chris Eagle noted, the sum "telescopes" and simplifies to $$p_1 - p_N,$$ so you could also write it that way, but that represents a different (and simpler) calculation that happens to always produce the same result.
