Determing range of x for which series converges or diverges

[pablito21]

im trying to solve this excersice but i couldn't find any similar questions like this one

find for which real x the series SIGMA x^n/1+x^2n converges and for which it diverges

 

[mathman]

Your expression involving x is ambiguous. I suggest you put parentheses into clarify the order for division and addition.

 

[AlphaNumeric]

Assuming it's supposed to be $$\sum_{n=1}^{infinity} \frac{x^{n}}{1+x^{2n}}$$, you can use the ratio test to compute when it's convergent or not. Just by judging 'large n behaviour' you should be able to narrow down the possible interesting values of x pretty quickly.