What is `Sigma_(r=0)^(n) C(n,r)` equal to ?

What is sum_(r=0)^(1) ""^(n+r)C_(n) 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 ?

If Sigma_(r=1)^(n) r^4=I(n), " then "Sigma__(r=1)^(n) (2r -1)^4 is equal to

If Sigma_(r=1)^(n) r^4=I(n), " then "Sigma__(r=1)^(n) (2r -1)^4 is equal to

If Sigma_(r=1)^(2n) sin^(-1) x^(r )=n pi, then Sigma__(r=1)^(2n) x_(r ) is equal to

If Sigma_(r=1)^(2n) sin^(-1) x^(r )=n pi, then Sigma__(r=1)^(2n) x_(r ) is equal to

If S_(n)=Sigma_(r=1)^(n)t_(r)=(1)/(6)n(2n^(2)+9n+13) , then Sigma_(r=1)^(n)sqrt(t_(r)) is equal to

If S_(n)=Sigma_(r=1)^(n)t_(r)=(1)/(6)n(2n^(2)+9n+13) , then Sigma_(r=1)^(n)sqrt(t_(r)) is equal to

If Sigma_(r=1)^(n) cos^(-1)x_(r)=0, then Sigma_(r=1)^(n) x_(r) equals