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

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

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

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

underset(n to oo)lim (1+3+6+...+n(n+1)//2)/(n^(3))=

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

underset(n to oo)lim (1+3+5+....+(2n-1))/(2+4+6+..2n)

underset(n to oo)lim (1^(3)+2^(3)+3^(3)+...+n^(3))/(n^(4))=

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

Find underset(n to oo)lim ((2n^(3))/(2n^(2)+3)+(1-5n^(2))/(5n+1))

Evaluate : underset(n to oo) lim[((1+1^(2)/n^(2)))(1+(2^(2))/(n^(2)))(1+(3^(2))/(n^(2)))…(1+(n^(2))/(n^(2)))]^((1)/(n))