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

Let a = lim_(n rarr oo) (1+2+3+.....+n)/(n^(2))= , b = lim_(n rarr oo) (1^(2)+2^(2)+.....+n^(2))/(n^(3))= then

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

Evaluate : lim_(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim_(n->oo) (1^3+2^3+...+n^3)/n^5

Evaluate the following limits : Lim_(n to oo) (1+2+3+...+n)/(n^(2)) ( or Lim_(x to oo) (Sigman)/(n^(2)))

The value of lim_(x to oo) (1 + 2 + 3 … + n)/(n^(2)) is

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

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

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

underset(n to oo)lim (1+2+3+...+n)/(n^(2))=