Evaluate the following limit: `(lim)_(n->oo)(1/(n^2)+2/(n^2)+3/(n^2)++(n-1)/(n^2\ ))`

Evaluate the following limit: (lim)_(n->oo)(1^3+2^3+ n^3)/((n-1)^4)

Evaluate the following limit: (lim)_(n->oo)2^(n-1)sin(a/(2^n))

Evaluate the following limit: (lim)_(n->oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

Evaluate the following limits : Lim_( n to oo) (1+2/n)^(2n)

Evaluate the following limit: lim_(nto oo)[(n!)/(n^(n))]^(1//n)

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

Evaluate the following limit: (lim)_(n->oo)(sin(a/(2^n)))/(sin(b/(2^(n\ ))))

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

Evaluate the following limits : Lim_(n to oo) (Sigman^(3))/(n^(4))

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is