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

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

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    $\begingroup$ That is a capital Sigma (from the Greek alphabet). It stands for "Sum". $\endgroup$ – lulu Sep 23 '17 at 19:41
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    $\begingroup$ @lulu thanks i have something to search on now. $\endgroup$ – user483856 Sep 23 '17 at 19:43
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    $\begingroup$ here is a good place to start. $\endgroup$ – lulu Sep 23 '17 at 19:44
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    $\begingroup$ 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, $$\sum_{k=1}^{n} x^k = x^1 + x^2 + x^3 + \cdots + x^n$$ $\endgroup$ – md2perpe Sep 23 '17 at 19:48
  • $\begingroup$ I'm very confused why you call it "romanian". $\endgroup$ – Rahul Sep 23 '17 at 20:38
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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 $$ \sum_{i=1}^4 i = 1 + 2 +3+4 = 10. $$

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  • $\begingroup$ 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). $\endgroup$ – student Sep 28 '17 at 19:09

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