(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

3. 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!

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# Homework Help: Determine Series Convergence Given Convergence of a Power Series

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