Power Series

Find the radius and interval of convergence for each of the following power series.

1. \(\displaystyle{\sum_{n=1}^{\infty}(-1)^n\,\frac{x^n}{n^3}}\) Solution ↗
2. \(\displaystyle{\sum_{n=1}^{\infty}\frac{n^2x^n}{2^n}}\) Solution ↗
3. \(\displaystyle{\sum_{n=1}^{\infty}\frac{n^3}{4^n}x^n}\) Solution (Image) ↗
4. \(\displaystyle{\sum_{n=1}^{\infty}\frac{(x-5)^n}{n}}\) Solution ↗
5. \(\displaystyle{\sum_{n=1}^{\infty}(-1)^n \frac{ n^2\, x^n}{2^n}}\) Solution ↗
6. \(\displaystyle{\sum_{n=1}^{\infty} \frac{ (x+2)^n}{4^n}}\) Solution ↗
7. \(\displaystyle{\sum_{n=0}^{\infty}\frac{3^n\,x^n}{2n^3+10}}\) Solution ↗
8. \(\displaystyle{\sum_{n=1}^{\infty}\frac{(x+2)^n}{n^2\,3^n}}\) Solution ↗
9. \(\displaystyle{\sum_{n=1}^{\infty}n^n\, x^n}\) Solution ↗
10. \(\displaystyle{\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n+1}}{(2n+1)!} }\) Solution ↗