`lim_(n->oo)1/n[tan (pi/(4n))+tan((2 pi)/(4n))+...tan((npi)/(4n))]`

The value of lim_(n rarr oo)[tan((pi)/(2n))tan((2 pi)/(2n))......tan((n pi)/(2n))]^((1)/(n))

lim_ (n rarr oo) (1) / (n) [tan ((pi) / (4n)) + tan ((2 pi) / (4n)) + ... tan ((n pi) / (4n) )]

Evaluate: (lim_(n rarr oo)n cos((pi)/(4n))sin((pi)/(4n))

Let f(x) be defined as f(x)=max{a,b,c} where a=lim_(n rarr oo)lim_(alpha rarr1^(+))(alpha^(n)|sin x|+|cos x| alpha^(-n))/(alpha^(n)+alpha^(-n)) , b=lim_(n rarr oo)lim_(alpha rarr1^(-))(alpha^(n)|sin x|+|cos x| alpha^(-n))/(alpha^(n)+alpha^(-n)) , c=lim_(n rarr oo)(pi)/(4n)[1+cos(pi)/(2n)+...+cos((n-1)pi)/(2n)] then The range of f(x) is

tan^(-1)((3)/(n))+tan^(-1)((4)/(n))=(pi)/(2)

If lim_(n rarr oo)(prod_(r=1)^(n)sin((r pi)/(4n))cos((r pi)/(4n)))^((1)/(n))=(a)/(b) a,b in N then find the least value of (a+b)

lim_( n to oo) (sin ""(pi)/(2n) . sin ""(2pi)/(2n). sin ""(3pi)/(2n)......sin""((n -1) pi)/(2n))^(1//n) is equal to