- #1
Poetria
- 267
- 42
Homework Statement
##f(x)=\sum_{n=0}^\infty x^n##
##g(x)=\sum_{n=253}^\infty x^n##
The radius of convergence of both is 1.
## \lim_{N \rightarrow +\infty} \sum_{n=0}^N x^n - \sum_{n=253}^N x^n##
2. The attempt at a solution
I got:
## \frac {x^{253}} {x-1}+\frac 1 {1-x}## for ##|x| \lt 1##
so the radius of convergence of the sum of these power series is just the same and equals 1?