2 sum ratio

[man111]

Evaluation of

[tex]\displaystyle \frac{\displaystyle\sum_{k=0}^r \binom nk \binom{n-2k}{r-k}}{\displaystyle\sum_{k=r}^n \binom nk \binom{2k}{2r}\left(\frac{3}{4}\right)^{n-k}\left(\frac{1}{2}\right)^{2k-2r}}[/tex], Where [tex]n\geq 2r[/tex]

[Гост]

man, oti tvoiti postcheta gi nema u angliiskata versija na forumo?

[man111]

Evaluation of

[tex]\displaystyle \frac{\displaystyle\sum_{k=0}^r \binom nk \binom{n-2k}{r-k}}{\displaystyle\sum_{k=r}^n \binom nk \binom{2k}{2r}\left(\frac{3}{4}\right)^{n-k}\left(\frac{1}{2}\right)^{2k-2r}}[/tex], Where [tex]n\geq 2r[/tex]

Friends , Please have a look on that problem , Thanks

[man111]

Friends have a look on that problem, Thanks

[man111]

Evaluation of

[tex]\displaystyle \frac{\displaystyle\sum_{k=0}^r \binom {n}{2k} \binom{n-2k}{r-k}}{\displaystyle\sum_{k=r}^n \binom nk \binom{2k}{2r}\left(\frac{3}{4}\right)^{n-k}\left(\frac{1}{2}\right)^{2k-2r}}[/tex], Where [tex]n\geq 2r[/tex]