Practice problem
Let r,a∈Rr, a \in \mathbb{R}r,a∈R. What is the interval of convergence for the following series? ∑n=0∞rn(x−a)n\sum_{n=0}^\infty r^n(x-a)^nn=0∑∞rn(x−a)n
(−1r+a,1r+a)(-\frac{1}{r}+a, \frac{1}{r}+a)(−r1+a,r1+a)
(−∞,1r+a)(-\infty, \frac{1}{r}+a)(−∞,r1+a)
[−1r+a,1r+a)[-\frac{1}{r}+a, \frac{1}{r}+a)[−r1+a,r1+a)
[−1r+a,1r+a][-\frac{1}{r}+a, \frac{1}{r}+a][−r1+a,r1+a]
This series cannot converge for any value of xxx.
Type a concept, like “slope” or “photosynthesis”.