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

The value of underset(r=1)overset9sum sin^2(rpi)/18 =

Find the value of overset(10)underset(i=1)sum(10xxi) .

The value of .^50c_4+underset(r=1)overset6sum.^(56-r)c_3 is

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

Prove that, underset(n=1)overset(oo)sum cot^(-1)(2n^(2))=(pi)/(4)

If R_(1) is the circumradius of the pedal triangle of a given triangle ABC, and R_(2) is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_(3), R_(4) ..., then the value of underset( i=1)overset(oo)sum R_(i) , where R (circumradius) of DeltaABC is 5 is

Prove that underset(r=1)overset(n)sum "tan"^(-1)(2r)/(r^(4)+r^(2)+2)="tan"^(-1)(n^(2)+n+1)-(pi)/(4)

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)))

Prove that the value of underset(r=0)overset10sum cos^3((rpi)/3) is equal to -1/8