Question

help....interval of convergence

Answer 1

how do i test where is converges or diverges

Answer 2

Use the ratio test. Compare the expressions of successive terms:
\[\lim_{n\to\infty}\left|\frac{(-1)^{n+1+1}x^{n+1}}{4^{n+1}}\times\frac{4^n}{(-1)^{n+1}x^n}\right|=\frac{|x|}{4}\]
What are the convergence conditions for the ratio test?