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Calculus II Quiz
#11 May
13, 2003
Name____________________ R. Hammack Score
______
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Find the interval of convergence of the folloing power series.
(1)
Using the ratio test for absolute convergence:
Thus, for convergence, we must have ,
or .
For x = 1/5, the series is which
is a convergent p-series. Thus the series converges for x
= 1/5.
For x = -1/5, the series is which
is a convergent alternating series. Thus the series converges for x
= -1/5.
Thus, the interval of convergence is .
(2)
Using the ratio test for absolute convergence:
Thus, for convergence, we must have ,
or .
For x = 1, the series is which
is divergent by comparison with the divergent harmonic series , as
.
For x = -1, the series is which
is a convergent alternating series. Thus the series converges for x
= -1.
Thus, the interval of convergence is .