Non-Inverting Amplifier Question

First let,

\(R_{N} = R_{N1}||...||R_{Nn}\)

\(R_{P} = R_{P1}||...||R_{P0}\)

I'm trying to find the effect the non-inverting terminal has on the output. I first ground the inverting terminal and call the equivalent resistance there RN.

Now I know that,

\(V_{oP} = (\frac{R_{f}}{R_{N}} + 1)V_{in}\)

Now that all that's left to do is find "Vin".

The current across Rp1 will be Vn1/Rp1 as follows for the current across Rpn, Vnn/Rpn.

Therefore by KCL the current across Rp0 to ground is the sum of all these currents, i0 = i1+...+in

So the voltage as seen by the non-inverting terminal is simply Rp0 * i0 or Rp0*[i1 +...+ in]

or equivalently,

\(V_{+} = R_{P0} * \left[ \frac{V_{p1}}{R_{P1}} + ... + \frac{V_{pn}}{R_{Pn}} \right]\)

but I'm having trouble converting this to the following form,

\(V_{oP} = (\frac{R_{f}}{R_{N}} + 1) \left[\frac{R_{P}*V_{p1}}{R_{P1}} + ... + \frac{R_{P}*V_{pn}}{R_{Pn}} \right] \)

I feel fairly confident I've got the work done right I just can't see how to switch between the two forms.

Any ideas?

EDIT: I found my mistake with currents i1 up to in, I was able to obtain the correct form now.