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I am trying to solve for $N_{mpn}$. Can this be solved? $$\sum_{i=1}^K\frac{V_id_iP_i}{1-e^{-V_id_iN_{mpn}}}=\sum_{i=1}^KV_id_in_i$$

In researching this, it did not appear that I could pull any constants out because every variable is part of the iteration. I do know that each side needs to be simplified in order to remove the summations, but I couldn't find a resource that could succinctly tell me how to simplify a summation that contained multiple variables, each one being directly iterated in the summation.

For example, I know that: $$\sum_{i=1}^N6yx_i=6y\sum_{i=1}^Nx_i$$

But it's not clear to me how to simplify something like: $$\sum_{i=1}^Ny_ix_iz_i$$

Let alone something like the left side of the equation. Frankly, I don't know where to start.

kbennett
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    Looks like numerical methods would be needed. – lulu Feb 06 '20 at 15:16
  • Welcome to MSE. In order to get responses that suit your needs, please include in the body of the question your own thoughts, the effort made so far, and the specific difficulties that got you stuck. – Lee David Chung Lin Feb 06 '20 at 15:31
  • Many thanks to Parcly Taxel for editing this to TeX commands. I appreciate your help. – kbennett Feb 06 '20 at 22:18

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