Sum from i=1 to N of ik^i (for Helix-Coil zipper model)

Couldn’t easily find a derivation of the sum:

Formulae 1

The result is on wikipedia (http://en.wikipedia.org/wiki/List_of_mathematical_series) but the derivation is not. Here is a version I wrote out quickly (click for full size):

Formulae 2

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1 comment
  1. John said:

    Or spot that it is the differential of a geometric series

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