`L t[1/(1-n^2)+2/(1-n^2)++n/(1-n^2)]i s` is equal to

If S= tan^(-1) ((1)/(n^(2) +n+1)) + tan^(-1) ((1)/(n^(2) + 2n+ 3))+ ….+ tan^(-1) ((1)/(1+(n+19) (n+20))) , then tan (s) is equal to

If (1-i)^n = 2^n , then n is equal to

If n in Z , then (2^(n))/(1+i)^(2n)+(1+i)^(2n)/(2^(n)) is equal to

The complex number 2^n/(1+i)^(2n)+(1+i)^(2n)/2^n , n epsilon I is equal to

If S_(1), S_(2) and S_(3) denote the sum of first n_(1) , n_(2) and n_(3) terms respectively of an A.P.L , then : (S_(1))/(n_(1)) . ( n _(2) - n_(3)) + ( S_(2))/( n_(2)). ( n _(3) - n_(1)) + ( S_(3))/( n_(3)) . ( n_(1) - n_(2)) is equal to :

The value of (n+2).^(n)C_(0).2^(n+1)-(n+1).^(n)C_(1).2^(n)+(n).^(n)C_(2).2^(n-1)-….." to " (n+1) terms is equal to