Find the value of `:^50C_4+sum_(r=1)^6 .^(56-r)C_3.`

The value of ""^(50)C_(4)+sum_(r=1)^(6)""^(56-r)C_(3) , is

If n is a positive integer and C_r = ""^nC_r then find the value of sum_(x = 1)^n r^2 ((C_r)/(C_(r - 1)) )

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

Find the value of lim_(n to oo) (tan(sum_(r=1)^(n) tan^(-1)((4)/(4r^(2)+3)))) .

Find the value of ""^(47)C_4+ underset (r=1) overset( 5) sum ""^(52-r)C_3

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

If z_r : r=1,2,3, ,50 are the roots of the equation sum_(r=0)^(50)z^r=0 , then find the value of sum_(r=0)^(50)1/(z_r-1)

The value of sum_(r=0)^(3n-1)(-1)^r ^(6n)C_(2r+1)3^r is

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