`lim_(n rarr oo)n sin\ (2 pi)/(3n)*cos\ (2 pi)/(3n)`

lim_(nto oo){n" sin"(2pi)/(3n)."cos"(2pi)/(3n)} =

lim_(n rarr oo)2^(n)sin(a)/(2^(n))

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

lim_(n rarr oo)(2^(3n))/(3^(2n))=

lim_(n rarr oo)(pi n)^(2/n) =

lim_ (n rarr oo) (pi) / (6n) [sec ^ (2) ((pi) / (6n)) + sec ^ (2) (2 * (pi) / (6n)) + .... ..... + sec ^ (2) ((n-1) (pi) / (6n)) + (4) / (3)]

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

lim_(n rarr oo)(n^(2))/(1+2+3+...+n)

lim_(n rarr oo)(n^(2))/(1+2+3+...+n)

lim_(n rarr oo)(n^(2))/(1+2+3+...+n)