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

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

Evaluate: lim_(n rarr oo) ((1^(2)+2^(2)+3^(2)+...+n^(2)))/((1+3+5+7+...+"n terms")) .

Evaluate: lim_(n rarr oo)((1^(2))/(n^(3))+(2^(2))/(n^(3))+(3^(2))/(n^(4))+...+(1)/(n))

Evaluate: lim_(n rarr oo) (n^(2)(1+2+3+4+......+n))/(n^(4)+4n^(2)) .

lim_(x rarr oo) (1+2/n)^(2n)=

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 rarr oo)(1^(2)+2^(2)+3^(2)+.........+n^(2))/(n^(3)) is equal to -

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

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

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