Syntax#

$\sum_{i = a}^{b} f(i)$

This means:
Start with $i = a$, increase $i$ by 1 until $i = b$, and sum all values of $f(i)$.

Example#

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

You can also include conditions:

$\sum_{\substack{i=1 \\ i \text{ odd}}}^{5} i = 1 + 3 + 5 = 9$

Syntax#

$\prod_{j = a}^{b} f(j)$

This means:
Multiply all values of $f(j)$ from $j = a$ to $j = b$.

Example#

$\prod_{j=1}^{4} j = 1 \cdot 2 \cdot 3 \cdot 4 = 24$

Just like summation, you can add conditions to exclude certain terms:

$\prod_{\substack{j=1 \\ j \ne 2}}^{4} f_j(x)$

This means: multiply all $f_j(x)$ from $j = 1$ to $4$, except when $j = 2$.