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Show that the HM of (2n+1)Cr and (2n+1)...

Show that the HM of (2n+1)C_r and (2n+1)C_(r+1)` is (2n+1)/(n+1)` times of `(2n)C_r` Also show that `sum_(r=1)^(2n-1) (-1)^(r-1)*r/(2nC_r)=n/(n+1)`.

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