`underset(n→∞)lim(n/(1+n))^(n)`

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

underset(n to oo)lim {1/(1-n^(2))+(2)/(1-n^(2))+....+(n)/(1-n^(2))} is equal to

If underset(n to oo)lim (1-(10)^(n))/(1+(10)^(n+1))=- alpha/10, then the value of alpha is

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

Value of underset(ntoinfty)(lim)((n+1)^(1//3)+(n+2)^(1//3)+…+(2n)^(1//3))/(n^(4//3)) is equal to

Prove that underset( n rarr oo)lim x_(n)=1, if x_(n)=(3^(n)+1)/3^(n) .

Taking advantage of the theorem on passing to the limit in inequalities, prove that underset(n to oo)lim x_(n)=1 if x_(n)=2n(sqrt(n^(2)+1)-n)