# Dose #sum ((n^2+3)/(2+n^2))^(n^3)# with #n = 0 -> # infinity converge ?

##### 1 Answer

Jun 5, 2017

No.

#### Explanation:

Use the n-th term test:

For any integer

#n# ,#(n^2+3)/(2+n^2)# will always be greater than 1.Therefore,

#((n^2+3)/(2+n^2))^(n^3)# will always be greater than 1 for any positive integer#n# .

This means that we can be sure that:

#lim_(n->oo)((n^2+3)/(2+n^2))^(n^3) >= 1#

Which means that

The series fails the n-th term test, and therefore diverges.