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What is the difference between $\Sigma $ and $ S_n $

Can they be used interchangeably? If not then when can they be interchanged?

William
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    In what context does your $S_n$ lie? It could be a lot of things and none of them seems remotely related to $\Sigma$. – Arnaud Mortier Jun 13 '18 at 16:45
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    @Arnaud Mortier Sn as in sum of n-terms? Maybe... – William Jun 13 '18 at 16:46
  • $ S_n $ is usually just a number. $\Sigma $ is used for general formulas and definitions – user29418 Jun 13 '18 at 16:47
  • @William "Maybe..." If you don't know, you can include a few lines from the book that you are reading, or whatever related information, so that people here can try and guess for you. Otherwise it is pretty difficult. The question does lack context. – Arnaud Mortier Jun 13 '18 at 17:11
  • @Arnaud Mortier That's exactly why I'm here sir, my text book doesn't explain much it sometimes uses the Sn formula and sometimes sigma.. I'm studying series if that helps? – William Jun 13 '18 at 17:13
  • Yes it does help, you should indicate it in the question along with an example. It is likely that Sean Robertson's answer below is appropriate then. – Arnaud Mortier Jun 13 '18 at 17:16

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We write $S_n$ to usually denote the partial sums of a sequence. The actual act of adding is indicated by the capital sigma, $\sum$.

For example, let $a_n = \frac{1}{2^n}$. Then $S_n = \sum_{j = 1}^n a_j$ is the $n$-th partial sum of the sequence $a_n$.

The capital sigma just tells us to add while $S_n$ gives a name to the partial sum.

Sean Roberson
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  • I'm new to series, so I'm not quite sure what is a partial sum (but I think I have a faint idea).. just to be sure that we are on the same page, the Sn I'm talking about is the one that has the formula $\frac{n}{2}[ 2a + (n-1)d] ... – William Jun 13 '18 at 17:16
  • Partial sums are like "running totals." So $S_1 = a_1$, and $S_2 = a_1 + a_2$, and $S_3 = a_1 + a_2 + a_3$... – Sean Roberson Jun 13 '18 at 17:17