___________________________________________________________
Calculus II Quiz
#9 May
9, 2005
Name_________________ R. Hammack Score
______
___________________________________________________________
(1) Find the
interval of convergence of the power series .
Using the ratio test for absolute convergence, we get
ρ====4|
x|=4|x|
For convergence, we need ρ=4|x|<1, so |x|
< 1/4, or -1/4 < x
< 1/4.
Check endpoint x = 1/4
==
(divergent p-series)
Check endpoint x = -1/4
==
(convergent alternating p-series)
Conclusion: The interval of convergence is [-,
)