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A Equality with binomials

  1. Dec 9, 2016 #1

    I am reading a paper and I am trying to understand an equality which is given without proof:
    [tex]\sum_{k=1}^s\binom{2s-k}{s}\frac{k}{2s-k}v^k(v-1)^{s-k}=v\sum_{k=0}^{s-1}\binom{2s}{k}\frac{s-k}{s}(v-1)^{k} [/tex]
    Here, s>0, k and v are positive integers.
    The equality in question appears in Lemma 2.1 of

    Would you be kind and give me some insights on how to derive this equality?

    Thank you,

  2. jcsd
  3. Dec 9, 2016 #2


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    Staff: Mentor

    I'm afraid you will have to expand the terms ##(v-1)^{n}## and some addition theorems on binomials. Perhaps an induction on ##s## can shorten the way.
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