Non Inverting Summing Amplifier

Here's the circuit:

Non Inverting Summing Amplifier, general case

We start by finding the equations for $V_{+}$ and $V_{-}$:
\[V_{-} = V_{out} \frac{R_g}{R_g +R_f}\]
The currents to the $V_{+}$ node have the same subscripts as the voltages and resistances. We now have a bunch of equations:
\[V_{1} - V_{+} = I_{1}R_{1}\\
V_{2} - V_{+} = I_{2}R_{2} \]
and so on to:
\[V_{n} - V_{+} = I_{n}R_{n} \]
We also have
\[I_{1}  +  I_{2} +\cdots + I_{n} = 0 \]

So by arranging the equations in this form:

\[\frac{V_{n} - V_{+}}{R_{n}} = I_{n} \]

we get:

\[\frac{V_{1} - V_{+}}{R_{1}}+\frac{V_{2} - V_{+}}{R_{2}}+\cdots +\frac{V_{n} - V_{+}}{R_{n}} = 0 \]
which can be simplified to:
\[V_{+}=\frac{V_{1}R_{1}R_{2}\cdots R_{n}/R_1+V_{2}R_{1}R_{2}\cdots R_{n}/R_2+\cdots +V_{n}R_{1}R_{2}\cdots R_{n}/R_n }{R_{1}R_{2}\cdots R_{n}/R_1+R_{1}R_{2}\cdots R_{n}/R_2+R_{1}R_{2}\cdots R_{n}/R_n}  \]
(Hope I got that notation right...)

Using the golden op amp rules we now set $V_{+}= V_{-}$ and get:
\[V_{out} \frac{R_g}{R_g +R_f}=\frac{V_{1}R_{1}R_{2}\cdots R_{n}/R_1+V_{2}R_{1}R_{2}\cdots R_{n}/R_2+\cdots +V_{n}R_{1}R_{2}\cdots R_{n}/R_n }{R_{1}R_{2}\cdots R_{n}/R_1+R_{1}R_{2}\cdots R_{n}/R_2+R_{1}R_{2}\cdots R_{n}/R_n} \Rightarrow \\
 V_{out} =\frac{R_g+R_f}{R_g } \frac{V_{1}R_{1}R_{2}\cdots R_{n}/R_1+V_{2}R_{1}R_{2}\cdots R_{n}/R_2+\cdots +V_{n}R_{1}R_{2}\cdots R_{n}/R_n }{R_{1}R_{2}\cdots R_{n}/R_1+R_{1}R_{2}\cdots R_{n}/R_2+R_{1}R_{2}\cdots R_{n}/R_n} \]
If we want to, we can simplify this drastically by setting one or both of these equations:
\[R_{1} = R_{2} = \ \cdots = R_{n} = R\\
R_{g} = R_{f}  \]
Will give us:
\[ V_{out} = 2  \frac{V_{1}+V_{2}+\cdots +V_{n} }{n} \]
To get a unity gain summer we can set:
\[\frac{R_g+R_f}{nR_g } = 1 \Rightarrow \\
R_f = Rg(n-1) \]

That's it. By the way, the schematics I made using xcircuit. It was my first circuit using this tool, but it seems nice enough to try it some more...