`cot^(-1)(2*1^(2))+cot^(-1)(2*2^(2))+cot^(-1)(2*3^(2))+... "upto "infty` is equal to

cot^(-1)(2.1^(2))+cot^(1)(2.2^(2))+cot^(-1)(2.3)^(2)+………… up to oo =

If the sum of first 16 terms of the series s=cot^(-1)(2^2+1/2)+cot^(-1)(2^3+1/(2^2))+cot^(-1)(2^4+1/(2^3))+ up to terms is cot^(-1)((1+2^n)/(2(2^(16)-1))) , then find the value of ndot

Find the sum to n terms of the series S_(n)=cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^(3)+(1)/(2^(2)))+cot^(-1)(2^(4)+(1)/(2^(3)))+..... upto n terms ?

If the sum of the series cot^(-1)2+cot^(-1)8+cot^(-1)18+…+cot^(-1)2n^(2)+…… " upto "infty " is "(kpi)/4 then the value of K is

If A = 1/1 cot ^(-1) (1/1) + 1/2 cot^(-1) (1/2) + 1/3 cot ^(-1) ( 1/3) " and " B = 1 cot^(-1) ( 1) + 2 cot^(-1) (2) + 3 cot^(-1) (3) " then " |B - A| " is equal to " (a pi )/b + c/d cot ^(-1) (3) where a,b,c,d in N are in their lowest form , find ( b -a - c - d)

If A = 1/1 cot ^(-1) (1/1) + 1/2 cot^(-1) (1/2) + 1/3 cot ^(-1) ( 1/3) " and " B = 1 cot^(-1) ( 1) + 2 cot^(-1) (2) + 3 cot^(-1) (3) " then " |B - A| " is equal to " (api)/b + c/d cot ^(-1) (3) where a,b,c,d in N are in their lowest form , find ( b -a - c - d)

If A = 1/1 cot ^(-1) (1/1) + 1/2 cot^(-1) (1/2) + 1/3 cot ^(-1) ( 1/3) " and " B = 1 cot^(-1) ( 1) + 2 cot^(-1) (2) + 3 cot^(-1) (3) " then " |B - A| " is equal to " (api)/b + c/d cot ^(-1) (3) where a,b,c,d in N are in their lowest form , find ( b -a - c - d)

cot^-1 (9/2) + cot^-1 (25/2) + cot^-1 (49/2) + ........ to n terms is equal to