# Thread: Power Series Once Again

1. ## Power Series Once Again

This stuff confuses me!!!

Find the radius and the interval of convergence of the power series.

$\displaystyle \sum_{n=1}^{\infty} \frac{(x+1)^n}{n}$

2. Originally Posted by larson
This stuff confuses me!!!

Find the radius and the interval of convergence of the power series.

$\displaystyle \sum_{n=1}^{\infty} \frac{(x+1)^n}{n}$
$\displaystyle f(x) = \sum_{n=1}^{\infty}(x+1)^{n-1}$

$\displaystyle g(x) = \int f(x) \, dx= \sum_{n=1}^{\infty}\frac{(x+1)^{n}}{n}$

The ROC for f(x) is $\displaystyle |x+1| < 1$

3. Originally Posted by larson
This stuff confuses me!!!

Find the radius and the interval of convergence of the power series.

$\displaystyle \sum_{n=1}^{\infty} \frac{(x+1)^n}{n}$
Originally Posted by Isomorphism
$\displaystyle f(x) = \sum_{n=1}^{\infty}(x+1)^{n-1}$

$\displaystyle g(x) = \int f(x) \, dx= \sum_{n=1}^{\infty}\frac{(x+1)^{n}}{n}$

The ROC for f(x) is $\displaystyle |x+1| < 1$
Or you could just apply the ratio test and force the limiting value to be less than 1 .....