How do you determine if the sum of 5^n/(3^n + 4^n)5n3n+4n from n=0 to infinity converges?

1 Answer
Jun 14, 2015

That sum diverges.

Explanation:

Since it is a sum of all positive numbers, it is regular (convergent or divergent, not irregular).

Since:

lim_(nrarr+oo)a_n=lim_(nrarr+oo)5^n/(3^n+4^n)=

lim_(nrarr+oo)5^n/4^n=lim_(nrarr+oo)(5/4)^n=+oo

(3^n is negligible respect 4^n)

and it is not 0, then it is divegent.