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

let underset(r=0)overset(2010)(sum)a_(r)x^(r)=(1+x+x^(2)+x^(3)+x^(4)+x^(5))^(402) and underset(r=0)overset(2010)(sum)a_(r)=a, then the value of ((underset(r=0)overset(2010)(sum)r.a_(r))/(underset(r=0)overset(2010)(sum)a_(r))) is equal to____.

Let n be a positive integer and (1+x)^(n)+C_(0)+C_(1)x+C_(2)x^(2)+C_(3)x^(3)+ . . .+C_(r)x^(r)+ . . .+C_(n-1)x^(n-1)+C_(n)x^(n) Where C_(r) stands for .^(n)C_(r) , then Q. The value of underset(r=0)overset(n)(sum)underset(s=0)overset(n)(sum),C_(r),C_(S) is

The value of cot[underset(n=1)overset(100)Sigmacot^(-1)(1+underset(k=1)overset(n)Sigma2k)] is

Find the value of sum_(r = 1)^(10) sum_(s = 1)^(10) tan^(-1) ((r)/(s))

underset(r=1)overset(n)sum ( r )/(r^(4)+r^(2)+1) is equal to

The value of underset( n rarroo)(lim) underset(r=1)overset(r=4n)(sum)(sqrt(n))/(sqrt(r ) (3 sqrt(r)+4)sqrt(n)^(2)) is equal to