(0) Find `lim_(n->oo) [ (1.2 +2.3 + .....+n(n+1)) / n^3]`

lim_(n->oo) (1.2+2.3+3.4+....+n(n+1))/n^3

lim_(n->oo) nsin(1/n)

Find the value of lim_(n->oo) (1+2+3+.......+n)/n^2

The value of lim_(n->oo) n^(1/n)

Find a for which lim_(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+(na+2)+...+(na+n)])=1/60

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

lim_(n->oo)2^(n-1)sin(a/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

Let f(x)= lim_(n->oo)(sinx)^(2n)

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