# Check my work? (series)

1. Nov 8, 2013

### xtrubambinoxpr

Find the interval of convergence for the power series $\sum$ $\frac{x^n}{\sqrt{n}}$

using the ratio test I get that the absolute value of x * the lim of square root of n over square root of n+1 = 0. so that being said i believe the interval of convergence is (-∞,∞) by the ratio test

Last edited: Nov 8, 2013
2. Nov 8, 2013

### vanhees71

$$\lim_{n \rightarrow \infty} \frac{a_n}{a_{n+1}}=\lim_{n \rightarrow \infty} \sqrt{\frac{n+1}{n}}=\cdots$$

3. Nov 8, 2013

### xtrubambinoxpr

Why? using the ratio test you get X^n+1 / sqrt(n+1) * the reciprocal of the original expression. So the x^n cancel out. leaving it in the form with n / n+1 square root

4. Nov 8, 2013

### xtrubambinoxpr

also i notice you have n+1 in the denominator. Isnt it the numerator in the original formula? thats how it is in my book anyways