I cuurently had a homework question that read as follows:

$\displaystyle a_n=n+(n+1)+(n+2)+.....+(2n)$

The question was to evaluate the first 4 terms. I came up with several ways I thought could be correct. For me it was I was not sure of the correct way of interpreting the math grammer. If I did exactly what it said I would wind up with infinity for every value of n. So I assumed that was not right and that it means to take the $\displaystyle \sum$ of n terms.

Are there any standard rules that help in deciphering this. Like rules of grammer for english or orders of operations in math. It seems that this "formula" in particular is ambiguous to me, so I assume I don't know the proper way of reading such. The way they switched the form of the terms realy threw me off. My nearest guess to a "rule" patern is as follows.

1) Individual terms will be grouped by parentheses. The n number will determine the amount of terms.

2) Sub in the number whereever you see it in the equation.

3) Always include the last term in the sumation if it differs from the form of the rest of the terms.

Are these correct statements of rules? If not could you advise me as to the correct rules, further if me rule list is not complete could you complete it?

I guessed three possibilities and one was right, But I would like to know the proper way of interpreting it. I am not interested in the answer to the above homework problem as I did get that resolved. I am interested in the principle behind it.