Question 920296
*[Tex \LARGE _{n}C_{r} = \frac{n!}{r!*(n-r)!}]




*[Tex \LARGE _{2n-1}C_{r} = \frac{(2n-1)!}{r!*((2n-1)-r)!}]




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{(2n-1)!}{(n-1)!*((2n-1)-(n-1))!}]




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{(2n-1)!}{(n-1)!*(2n-1-n+1)!}]




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{(2n-1)!}{(n-1)!*(n)!}]




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{2n(2n-1)!}{2n(n-1)!*(n)!}] Multiply top and bottom by 2n.




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{(2n)!}{2*(n(n-1)!)*(n)!}]




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{(2n)!}{2*(n)!*(n)!}]




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{(2n)!}{2*(n)!*(n)!}]




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{1}{2}*\frac{(2n)!}{n!*n!}]




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{1}{2}*\frac{(2n)!}{n!*(2n-n)!}]




*[Tex \LARGE _{2n-1}C_{n-1} = \frac{1}{2}*(_{2n}C_{n})]




*[Tex \LARGE 2*(_{2n-1}C_{n-1}) = \ \ \ _{2n}C_{n}]