The value of`underset(r=0)overset(10)sumr^(10)C_(r),3^(r).(-2)^(10-r)` is -

Find the value of underset(r = 0) overset(oo)sum tan^(-1) ((1)/(1 + r + r^(2)))

Find the value of underset(r = 1)overset(10)sum underset(s = 1)overset(10)sum tan^(-1) ((r)/(s))

The value of sum_(r=0)^(40) r""^(40)C_(r)""^(30)C_(r) is

The value of sum_(r=0)^(10) (-1)^(r).4^(10-r)""^(30)C_(r)""^(30-r)C_(10-r) is equal to

Prove that underset(r = 0) overset (n)(sum) 3^(r) ""^(n)C_(r) = 4^(n)

underset(r=0)overset(n)(sum)sin^(2)""(rpi)/(n) is equal to

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

Prove that underset(rles)(underset(r=0)overset(s)(sum)underset(s=1)overset(n)(sum))""^(n)C_(s) ""^(s)C_(r)=3^(n)-1 .

The value of sum_(r=0)^(3) ""^(8)C_(r)(""^(5)C_(r+1)-""^(4)C_(r)) is "_____" .

The number of positive zeros of the polynomial underset(j=0)overset(n)(Sigma)^n C_r(-1)^r x^r is