What is `C(n, r) + 2C(n, r - 1) + C(n, r - 2)` equal to?

Given that C(n, r) : C(n,r + 1) = 1 : 2 and C(n,r + 1) : C(n,r + 2) = 2 : 3 . What is P(n, r) : C(n, r) equal to ?

Given that C(n, r) : C(n,r + 1) = 1 : 2 and C(n,r + 1) : C(n,r + 2) = 2 : 3 . What is r equal to ?

Given that C(n, r) : C(n,r + 1) = 1 : 2 and C(n,r + 1) : C(n,r + 2) = 2 : 3 . What is n equal to ?

""^(n)C_(r)+2""^(n)C_(r-1)+C_(r-2) is equal to

""^(n)C_(r)+2""^(n)C_(r-1)+^(n)C_(r-2) is equal to

If C_0, C_1, C_2 ,……..C_n are the coefficient in the expansion of (1 + x)^n then show that C_0 C_r + C_1 C_(r + 1) + C_2 C_(r + 2) + ………..+ C_(n-r).C_n = ((2n)!)/((n-r)!(n+r)!)

sum_(r=1)^(n)(C(n,r))/(r+2) is equal to

""^(n-2)C_(r)+2.""^(n-2)C_(r-1)+""^(n-2)C_(r-2) is equal to