- #1
kdinser
- 337
- 2
I'm reviewing power series for use in differential equations and I'm having some trouble remembering how to deal with alternating series.
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.
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.