Is this mathematical syntax correct?
$\sum_{n+1}^m\sin(n-2) $
As you see, the starting value is $n+1$ instead of being just purely one variable.
Is this mathematical syntax correct?
$\sum_{n+1}^m\sin(n-2) $
As you see, the starting value is $n+1$ instead of being just purely one variable.
You have
$\sum_{n+1}^m\sin(n-2)$
What is the running index here? Apparently $\,n\,$ , but from what number does it begin running? Perhaps it should be $\,n=1\,$ in the summatory's lower limit?
As it stands, the expression makes not much sense.
If there's any doubt about what the index of summation is, then specify it explicitly. If you write about the sum of terms called $\sin(n-2)$, then commonplace conventions make the reader think $n$ goes from something to something. But you've used $n$ as one of the bounds, meaning $n$ stays put while some other variable goes from $n+1$ to $m$, and what that other variable, the index, is called (is it $i$? is it $k$?) you don't say. If you write $ \sum_{k=n+1}^m \sin(n-2), $ then that's $ \sin(n-2)+\sin(n-2)+\sin(n-2)+\cdots+\sin(n-2) $ and all terms are identical, and there are $m-n$ of them, so the sum is $(m-n)\sin(n-2)$. If you meant anything other than that, then don't use this notation.
I would say that your notation is not good. The reason is that it isn't clear what the index of summation is. From how it is written it looks like $m$ and $n$ might both be constants. But then you only have the variable $n$ after the summation sign, so one would think that $n$ is what is "changing" in the summation. But if you want the sum to start at $n+1$, then you should write something like (as mentioned in the comments and the other answer): $ \sum_{i = n+1}^m \sin(i-2). $ What this means is the sum $ \sin(n+1-2) + \sin(n+2-2) + \dots +\sin(m-1-2) + \sin(m-2). $ You could IMO get away with writing this same sum as $ \sum_{n+1}^m \sin(i-2). $