I have come across this symbol a few times, and I am not sure what it "does" or what it means: $\Large\sum$
What does the math notation $\sum$ mean?
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3Usually it is used for a sum. See this Wikipedia entry for [summation](http://en.wikipedia.org/wiki/Summation#Capital-sigma_notation) – 2011-04-11
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0Symbolic computation, while sharing the same first word as your question does not quite relate, retagged to notation. – 2011-04-11
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9Since nobody has mentioned it, this is the capital Greek letter, sigma, which is the Greek equivalent of the letter S. As others have noted, it is used to represent sums. – 2011-04-11
2 Answers
Here I use it once to explain what it does.
$$\sum_{i=1}^{5} i=1+2+3+4+5$$
Which translates to, sum over $i$, where $i$ starts at $1$ and goes to $5$. or this case
$$\sum_{i=1}^{5} i^2=1^2+2^2+3^2+4^2+5^2$$
Which translates to sum over the values of $i$, which range from $1$ to $5$ the function $i^2$.
Naturally one may wonder what if it is a product we are after, for example how do I represent $1\times2\times3\times4\times5$ or $1^2\times2^2\times3^2\times4^2\times5^2$
The notation for those are
$$\prod_{i=1}^5 i $$
and
$$\prod_{i=1}^5 i^2 $$
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0Just curious, as a high scool student, what is that Greek letter called? – 2011-12-23
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2@Hidde: $\Sigma$ is the upper-case Greek letter sigma (lower case: $\sigma$). $\Pi$ is the upper-case Greek letter pi (which you may know better in lower case, $\pi$). – 2011-12-23
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3Thanks! Kind of logical now that I think of it, P for Product, just as S for Sum :). – 2011-12-23
Coming from a programming background, I found it quite helpful to explain it using a for loop:
The mathematician would write it like this:
$\sum\limits_{i=m}^n f(i)$
And the programmer would write it like this:
result = 0 for (i=m; i<=n; i++) { result += f(i) }
You can think of m
as the start index
and n
as the end index
.