Find limits x->+infty of [(x+1)*((x^2)+1)*...*((x^n)+1)]/[(((n*x)^n)+1)^((n+1)/2)]

[jordan195]

Find limits x->+infty of [(x+1)*((x^2)+1)*...*((x^n)+1)]/[(((n*x)^n)+1)^((n+1)/2)]

Solve this limit without L'Hôpital's rule:
I'm always stuck on problems with limes. Can someone please help me with this ?

 

[MarkFL]

Hint: look at the degrees of the resulting polynomials in the numerator and denominator. If they are the same, then look at the ratio of the leading coefficients (the coefficients of the terms of highest degree).