This stuff confuses me!!! Find the radius and the interval of convergence of the power series. $\displaystyle \sum_{n=1}^{\infty} \frac{(x+1)^n}{n}$
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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 $\displaystyle |x+1| < 1$
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 .....
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