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

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

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

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

Equation x^(n)-1=0,ngt1,ninN, has roots 1,a_(1),a_(2),...,a_(n),. The value of underset(r=2)overset(n)sum(1)/(2-a_(r)), is

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

The value of ""^(50)C_4 + underset(r=1) overset(6)sum ""^(56-r)C_3 is

Find underset(r=0) overset(10)sumr^ (10)C_(r).3^(r).(-2)^(10-r)

Find the value underset(n rarr oo)("lim") underset(k =2)overset(n)sum cos^(-1) ((1 + sqrt((k -1) k(k + 1) (k + 2)))/(k(k + 1)))

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

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____.