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user64494
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This is mechanized in Maple:

binomial(m+n, n)*(sum(binomial(m, k)n(-1)^k/(n+k), k = 0 .. m))

binomial(m+n, n)*(sum(binomial(m, k)*n*(-1)^k/(n+k), k = 0 .. m));

$${\frac {{m+n\choose n}}{{m+n\choose m}}}$$ PS. Please, don't change my answer.

This is mechanized in Maple:

binomial(m+n, n)*(sum(binomial(m, k)n(-1)^k/(n+k), k = 0 .. m))

$${\frac {{m+n\choose n}}{{m+n\choose m}}}$$

This is mechanized in Maple:

binomial(m+n, n)*(sum(binomial(m, k)*n*(-1)^k/(n+k), k = 0 .. m));

$${\frac {{m+n\choose n}}{{m+n\choose m}}}$$ PS. Please, don't change my answer.

Source Link
user64494
  • 3.5k
  • 14
  • 22

This is mechanized in Maple:

binomial(m+n, n)*(sum(binomial(m, k)n(-1)^k/(n+k), k = 0 .. m))

$${\frac {{m+n\choose n}}{{m+n\choose m}}}$$