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((n C_r)/((r+3)C_3))

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

Find the sum sum_(r=0)^n(-1)^r*(""^nC_r)/(""^(r+3)C_r)

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

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)^(r) (""^(n)C_(r))/(""^(r+2)C_(r)) is equal to .

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

Find the sum sum_(r=1)^n r^2(^n C_r)/(^n C_(r-1)) .

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