Question

Convergence & divergence...
I'm studying for my Calc. quiz tomorrow and I am still confused by the concept of convergence when talking about series.
A question I reviewed went over the steps for finding the interval of convergence, which is fine- I understand. But then it asks to "Explain why the power series in [the example] diverges if x [is outside the interval of convergence]."
Thanks guys

Answer 1

It'd be easier to explain if you'd posted the actual example/question.

If x is outside the interval of convergence, then the terms of the series probably don't approach zero/a limit for that x, or don't approach zero 'fast enough' for the series to converge.

http://tutorial.math.lamar.edu/Classes/CalcII/PowerSeries.aspx

eg basic example: for x^n, if x = 2, then the terms approach inf as n approaches inf. If x = 0.1, the terms approach zero.