Difference between Summation and Sn

Question

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

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

Answer 1

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.