I'm reviewing power series for use in differential equations and I'm having some trouble remembering how to deal with alternating series.(adsbygoogle = window.adsbygoogle || []).push({});

For instance, if I have:

[tex]\sum(-1)^n(\frac{3}{2})^n[/tex]

if [tex]a_n=(\frac{3}{2})^n[/tex]

This fails the alternate series test because the limit of [tex]a_n[/tex] as n goes to infinity doesn't equal 0.

Can I group the (-1)^n into the fraction and call it a geometric series? In that case, it would diverge, |r| would be greater then 1.

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# Homework Help: Alternate series question

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