If `f(n)=sum_(r=1)^(n) r^(4)`, then the value of `sum_(r=1)^(n) r(n-r)^(3)` is equal to

sum_(r=1)^n r (n-r +1) is equal to :

sum_(r=1)^n r (n-r +1) is equal to :

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

sum_(r=1)^n r(n-r) is equal to :

sum_(r=1)^n r(n-r) is equal to :

If sum_(r=1)^(n)r^(4)=F(x), then prove that the value of sum_(n=1)^(n)r(n-r)^(3) is (1)/(4)[n^(3)(n+1)^(2)-4F(x)]

Let sum_(r=1)^(n)r^(4)=f(n)," then " sum_(r=1)^(n) (2r-1)^(4) is equal to

sum_(r = 1)^(n) r. r! is equal to

The value of sum_(r=1)^(n)(""^(n)P_(r))/(r!) is