`sum_(r=1)^oocot^(- 1)(r^2+3/4)=` (A) `pi/2` (B) `cot^-1 (2)` (C) `pi/6` (D) `tan^-1 (2)`

lim_(n to oo)sum_(r=1)^(n)cot^(-1)(r^(2)+3//4) is (a) 0 (b) tan^(-1)1 (c) tan^(-1)2 (d) None of these

The value of sum_(r=1)^oocot^(- 1)((r^2)/2+15/8) is equal to

tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3)) is equal to (A) pi (B) -pi/2 (C) 0 (D) 2sqrt(3)

The value of sum_(r=1)^(10)tan^(-1)(3/(9r^2+3r-1)) is a) cot^(-1)""13/6 b) tan^(-1)""13/6 c) cot^(-1)""14/5 d) tan^(-1)""14/5

If sum_(r=1)^(oo) cot^(-1)(((r+1)^(2))/(2))=tan^(-1)x then x is equal to

sum_(r=1)^oo tan^-1((6^r)/(2^(2r+1)+3^(2r+1)))

sin^-1 (-1/2)+tan^-1 (sqrt(3))= (A) -pi/6 (B) pi/3 (C) pi/6 (D) none of these

sin^-1 (-1/2)+tan^-1 (sqrt(3))= (A) -pi/6 (B) pi/3 (C) pi/6 (D) none of these

sum_(r=1)^(n) tan^(-1)(2^(r-1)/(1+2^(2r-1))) is equal to a) tan^(-1)(2^n) b) tan^(-1)(2)^n-pi/4 c) tan^(-1)(2^(n+1)) d) tan^(-1)(2^(n+1))-pi/4

If a=sum_(r=1)^oo(1/r)^2, b=sum_(r=1)^oo1/((2r-1)^2), then a/b= (A) 5/4 (B) 4/5 (C) 3/4 (D) none of these