# How to use math symbols to represent a basic formula

I've a fomula that looks like this:

How to properly represent this formula using SUM Symbol and MEAN symbol? $$r=2 \left(3(f_1) +\frac{(g_1+...+ g_n)}{n} + \frac{s_1 +... + s_n}{n}\right) + x_1 + y_1$$

I don't know how to represent this in math symbols. I know that the hole form is a sum and i also know that i'm calculating the mean whem i perform a sum of n numbers and i divide it by n.

• You divide the sum of two elements only, seemingly, twice. Or, did you mean $g_1+g_2+g_3+\dots+g_n$ instead of '(g1 + gN)'? – Berci Jan 5 '14 at 20:21
• yeah you get it right: i mean g1+g2+g3+⋯+gn – Lothre1 Jan 5 '14 at 20:22
• Is the N in gN supposed to be the same as the n in the denominator? So that (g1 + … + gN)/n is the mean of the g's? – MJD Jan 5 '14 at 20:25
• yes. you were right – Lothre1 Jan 5 '14 at 20:45

$$\frac{(g_1+...+g_N)}{n}=\frac{\sum_{i=1}^{n} g_i}{n}$$ $$\frac{(s_1+...+s_N)}{n}=\frac{\sum_{i=1}^{n} s_i}{n}$$ so,
$$r=2\left(3(f_1)+2 \left( \frac{\sum_{i=1}^{n} g_i}{n}\right)+\left(\frac{\sum_{i=1}^{n} s_i}{n}\right)\right)+x_1+y_1$$
The mean of some elements $g_1,g_2,\dots,g_n$ is often denoted by $\bar g$, you can introduce it by a sum notation. $$\bar g:=\frac{\sum_{k=1}^ng_k}n=\frac{g_1+g_2+\dots+g_n}n\,.$$
• $k$ is a "dummy" variable, like a loop index in programming, going from 1 to $n$. – hardmath Jan 5 '14 at 20:28