Question

How to get convergence interval for :
\[\sum_{n=1}^{\infty}(x ^{n-1})/(1+x^{n})\]

Answer 1

Call a_n the nth term. Then the series converges if
lim a_n+1 / a_n < 1

Use that condition to find for which x to does converge.

Answer 2

what i get is:
\[x*\lim[ (1+x^{n})/(1+x^{n-1}) < 1\]
how to properly get rid of the limit?

Answer 3

The same way you ever would; in other words, if you asked to evaluate that limit, I'm sure you could find it.

Answer 4

divide top and bottom by x^n-1