`lim_(n rarr oo)(1+2^(4)+3^(4)+...+n^(4))/(n^(5))`

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

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

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

" If "lim_(n rarr oo)((1^(2)+2^(2)+......+n^(2))(1^(4)+2^(4)+...+n^(4)))/((1^7+2^7+......+n^7))=(K+1)/(15);" then "K" is equal to "

lim_(n rarr oo)((1^(4))/(1^(5)+n^(5))+(2^(4))/(2^(5)+n^(5))+(3^(4))/(3^(5)+n^(5))+--+(n^(4))/(n^(5)+n^(5)))

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

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

If P=lim_(n rarr oo)(ea^(2)*e^(3)a^(4)...e^(n-1)a^(n))^((1)/(n^(2)+1)) then P^(4) equals