`lim_(n->oo)(sin((a)/(2^n)))/(sin((b)/(2^(n+1))))=`

Evaluate the following limit: quad sin((a)/(2^(n)))(lim)_(n rarr oo)(sin((a)/(2^(n))))/(sin((b)/(2^(n))))

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

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

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

lim_(n rarr oo)(1-(2)/(n))^(n)

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) (1 + sin ((a) / (n))) ^ (n)

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

Evaluate lim_(nrarroo)(2)/(n)(sin.(pi)/(2n)+sin.(2pi)/(2n)+sin.(3pi)/(2n)+....+sin.(npi)/(2n))

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0