- #1
BraedenP
- 96
- 0
Homework Statement
I am asked to comment on the convergence/divergence of three series based on some given information about a power series:
[tex]\sum_{n=0}^{\infty}c_nx^n[/tex] converges at x=-4 and diverges x=6.
I won't ask for help on all of the series, so here's the first one:
[tex]\sum_{n=0}^{\infty}c_n[/tex]
Homework Equations
The Attempt at a Solution
I tried reasoning that the question is suggesting a convergence interval of (-14,6) for the power series (I took -4 as the center, and 6 as the right-hand side) but the more I read the question, I don't think that's what it's suggesting. It's just commenting about divergence at those two exact points.
So now I'm stuck. Am I supposed to figure out the value of [itex]c_n[/itex] and work out the divergence of other series that way, or is there some way for me to compare these series using what I know about their centers of convergence (both are centered around 0).
Guidance would be awesome!