`sum_(n=1)^oo sin^-1( (sqrt(n)-(sqrt(n-1)))/(sqrt((n)(n+1)) )=` (A) `pi/4` (B) `pi/2` (C) `- pi/3` (D) `pi/3`

sum_(n=1)^(oo)(1)/(sqrt(n)+sqrt(n+1))

lim_(n rarr oo)((sqrt(n+3)-sqrt(n+2))/(sqrt(n+2)-sqrt(n+1)))

sin^(-1)sqrt((2-sqrt(3))/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)(sqrt(2))= (a) 0 (b) pi/4 (c) pi/6 (d) pi/2

sum_(n=1)^(oo)((1)/(4n-3)-(1)/(4n-1))=(pi)/(n) find n

sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to tan^(-1)(sqrt(n))-(pi)/(4)tan^(-1)(sqrt(n+1))-(pi)/(4)tan^(-1)(sqrt(n))(d)tan^(-1)(sqrt(n)+1)

lim_(n rarr oo)(sin(1)/(sqrt((n))))((1)/(sqrt(n+1)))^(+(1)/(sqrt(n+2))+(1)/(sqrt(n+2)))

lim_ (n rarr oo) sum_ (n = 1) ^ (n) (sqrt (n)) / (sqrt (r) (3sqrt (r) + 4sqrt (n)) ^ (2))

lim_(x rarr1^(-))(sqrt(pi)-sqrt(2sin^(-1)x))/(sqrt(1-x))=(A)sqrt((2)/(pi))(B)sqrt((pi)/(2))(C)(1)/(pi)(D)sqrt((1)/(pi))

The value of lim_(n rarr oo)sum_(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+sqrt(n))^(2)) is equal to (1)/(35) (b) (1)/(4)(c)(1)/(10) (d) (1)/(5)

The value of cos^(-1)sqrt((2)/(3))-cos^(-1)((sqrt(6)+1)/(2sqrt(3))) is equal to (A)(pi)/(3)(B)(pi)/(4)(C)(pi)/(2)(D)(pi)/(6)])