6

I have a simple question: what does the following mean?

$$\displaystyle\sum_{k=0}^n$$

Rodrigo de Azevedo
  • 1
  • 6
    That is a capital Sigma (from the Greek alphabet). It stands for "Sum". – lulu Sep 23 '17 at 19:41
  • 2
    @lulu thanks i have something to search on now. –  Sep 23 '17 at 19:43
  • 2
    here is a good place to start. – lulu Sep 23 '17 at 19:44
  • 1
    In this case, with $k=0$ below it and $n$ above, it means that the expression to the right of $\sum$ should be evaluated for $k=0, 1, 2, \ldots, n$ and then summed. For example, $$\sum_{k=1}^{n} x^k = x^1 + x^2 + x^3 + \cdots + x^n$$ – md2perpe Sep 23 '17 at 19:48
  • I'm very confused why you call it "romanian". –  Sep 23 '17 at 20:38
  • One thing to note is that even though it is similar to the Latin character E, it has nothing to do with it, and makes the same sound as the Latin character "S". – Duncan Ramage Sep 28 '17 at 19:08
  • This symbol is required to denote summations when the number of terms is too large for explicit expansion, or when it is variable (so impossible to write down). You have a similar symbol for products, using the capital pi letter: $\prod$. –  Jan 18 '22 at 15:23

1 Answers1

9

This symbol is a Greek letter called (capital) sigma. It's used to denote sums. The definition is

$$ \sum_{i=1}^n a_i = a_1+\cdots+a_n. $$

For example: $$ \sum_{i=1}^6 1 = \underbrace{1+\cdots+1}_{\text{6 times}} = 6 $$

or $$ \sum_{i=1}^4 i = 1 + 2 +3+4 = 10. $$

Epiousios
  • 3,194
  • One could add that in typed math, the summation sign $\sum$ and the capital Sigma $\Sigma$ are rarely exactly the same. I'm not sure how widespread this is for handwriting though (I have different symbols, but some colleagues definitely haven't). –  Sep 28 '17 at 19:09