Power series: Find the radius and interval of convergence of
the following power series.
- \(\displaystyle{\sum_{n=1}^{\infty}(-1)^n\,\frac{x^n}{n^3}}\)
solution
- \(\displaystyle{\sum_{n=1}^{\infty}\frac{n^2x^n}{2^n}}\)
solution
- \(\displaystyle{\sum_{n=1}^{\infty}\frac{n^3}{4^n}x^n}\)
solution
- \(\displaystyle{\sum_{n=1}^{\infty}\frac{(x-5)^n}{n}}\)
solution
- \(\displaystyle{\sum_{n=1}^{\infty}(-1)^n \frac{ n^2\,
x^n}{2^n}}\)
solution
- \(\displaystyle{\sum_{n=1}^{\infty} \frac{ (x+2)^n}{4^n}}\)
solution
-
\(\displaystyle{\sum_{n=0}^{\infty}\frac{3^n\,x^n}{2n^3+10}}\)
solution
- \(\displaystyle{\sum_{n=1}^{\infty}\frac{(x+2)^n}{n^2\,3^n}}\)
solution
- \(\displaystyle{\sum_{n=1}^{\infty}n^n\, x^n}\)
solution
- \(\displaystyle{\sum_{n=0}^{\infty} (-1)^n
\frac{x^{2n+1}}{(2n+1)!} }\)
solution
