" Prove that "(3!)/(2(n+3))=sum_(r=0)^(n)(-1)^(r)((^(n)C_(r))/(r+3)C_(r))

Prove that (3!)/(2(n+3))=sum_(r=0)^(n)(-1)^(r)((^nC_(r))/(r+3C_(r)))

Prove that (3!)/(2(n+3))=sum_(r=0)^n(-1)^r((n C_r)/((r+3)C_3))

Prove that sum_(r=0)^(n)r(n-r)C_(r)^(2)=n^(2)(^(2n-2)C_(n))

Prove that sum_(r=0)^(s)sum_(s=1)^(n)C_(s)^(n)C_(r)=3^(n)-1

sum_(r=1)^(n)(1)/((r+1)(r+2))*^(n+3)C_(r)=

If n in N, then sum_(r=0)^(n) (-1)^(r) (""^(n)C_(r))/(""^(r+2)C_(r)) is equal to .

Prove the following: sum_(r =0)^(n)(-1)^(r ) (3r+5).C_(r )=0

If n is a positive integer, prove that sum_(r=1)^(n)r^(3)((""^(n)C_(r))/(""^(n)C_(r-1)))^(2)=((n)(n+1)^(2)(n+2))/(12)

If n in N, then sum_(r=0)^(n) (-1)^(n) (""^(n)C_(r))/(""^(r+2)C_(r)) is equal to .