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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.

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    It may even be legal, depends on the judge. But it is a really bad idea to use $n$ as the (presumed) summation index, and also as a component of one of the ends. If I am reading your intent correctly, I would write something like $\displaystyle\sum_{i=n+1}^m \sin(i-2)$.2012-09-23

3 Answers 3

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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.

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    @user1561559 Then you probably want $\sum_{i=n+1}^m\sin(i-2)$ unless the expression you are going for is equal to $(m-n-1)\sin(n-2)$.2012-09-23
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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.

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    IMO, the index of summation should be specified explicitly even when there can't really be any doubt – really, it's just one symbol! The _range_ over which that variable is summed, which may be rather more awkward to write, may be well be left out if it's clear from the context like in $\langle a, b \rangle = \sum_i a_i\!\cdot\!b_i$. (Which, of course, you might write simply $a_ib_i$, following Einstein convention...)2012-09-23
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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). $