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

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

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

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

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

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

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

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

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

lim_(n rarr oo)(e^(2n)(n!)^(2))/(2n^(2n+1))

The value of lim_(n rarr oo) (1 + 2^(4) + 3^(4) +…...+n^(4))/(n^(5)) - lim_(n rarr oo) (1 + 2^(3) + 3^(3) +…...+n^(3))/(n^(5)) is :